Exhibit 10.4

OMNIBUS AGREEMENT

BY AND AMONG

WESTERN GAS EQUITY PARTNERS, LP

WESTERN GAS EQUITY HOLDINGS, LLC

AND

ANADARKO PETROLEUM CORPORATION

OMNIBUS AGREEMENT

This Omnibus Agreement (“Agreement”) is entered into on, and effective as of, the Closing Date (as defined herein), and is by and among Western Gas Equity Partners, LP, a Delaware limited partnership (the “Partnership”), Western Gas Equity Holdings, LLC, a Delaware limited liability company (the “General Partner”), and Anadarko Petroleum Corporation, a Delaware corporation (“Anadarko”). The above-named entities are sometimes referred to in this Agreement each as a “Party” and collectively as the “Parties.”

R E C I T A L S:

The Parties desire by their execution of this Agreement to evidence their understanding, as more fully set forth in Article II of this Agreement, with respect to the agreement of Anadarko to provide or cause to be provided, and the agreement of the Partnership to reimburse and compensate Anadarko for the provision of, certain general and administrative services.

In consideration of the premises, covenants, conditions, and agreements contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereby agree as follows:

ARTICLE I

DEFINITIONS

1.1 Definitions. (a) Capitalized terms used herein but not defined shall have the meanings given them in the Partnership Agreement.

(b) As used in this Agreement, the following terms shall have the respective meanings set forth below:

“Administrative Fee” is defined in Section 2.1(c).

“Affiliate” means, with respect to any Person, (a) any other Person directly or indirectly controlling, controlled by or under common control with such Person, (b) any Person owning or controlling fifty percent (50%) or more of the voting interests of such Person, (c) any officer or director of such Person, or (d) any Person who is an officer, director, trustee, or holder of fifty percent (50%) or more of the voting interest of any Person described in clauses (a) through (c). For purposes of this definition, the term “controls,” “is controlled by” or “is under common control with” shall mean the possession, direct or indirect, of the power to direct or cause the direction of the management and policies of a Person, whether through the ownership of Voting Securities, by contract or otherwise.

“Agreement” means this Omnibus Agreement, as it may be amended, modified or supplemented from time to time in accordance with the terms hereof.

“Anadarko” is defined in the preamble to this Agreement.

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“Anadarko Entities” means Anadarko and any other Person controlled by Anadarko other than the Partnership Entities. For purposes of this definition, “control” means the possession, direct or indirect, of the power to direct or cause the direction of the management and policies of a Person, whether through ownership of Voting Securities, by contract or otherwise.

“Change of Control” means, with respect to any Person (the “Applicable Person”), any of the following events: (i) any sale, lease, exchange or other transfer (in one transaction or a series of related transactions) of all or substantially all of the Applicable Person’s assets to any other Person, unless immediately following such sale, lease, exchange or other transfer such assets are owned, directly or indirectly, by the Applicable Person; (ii) the dissolution or liquidation of the Applicable Person; (iii) the consolidation or merger of the Applicable Person with or into another Person pursuant to a transaction in which the outstanding Voting Securities of the Applicable Person are changed into or exchanged for cash, securities or other property, other than any such transaction where (A) the outstanding Voting Securities of the Applicable Person are changed into or exchanged for Voting Securities of the surviving Person or its parent and (B) the holders of the Voting Securities of the Applicable Person immediately prior to such transaction own, directly or indirectly, not less than a majority of the outstanding Voting Securities of the surviving Person or its parent immediately after such transaction; and (iv) a “person” or “group” (within the meaning of Sections 13(d) or 14(d)(2) of the Exchange Act) other than Anadarko or any Affiliate of Anadarko becomes the “beneficial owner” (as defined in Rules 13d-3 and 13d-5 under the Exchange Act) of more than 50% of all of the then outstanding Voting Securities of the Applicable Person, other than in a merger or consolidation which would not constitute a Change of Control under clause (iii) above.

“Closing Date” means the date of the closing of the initial public offering of Common Units.

“CP Index” is defined in Section 2.1(c).

“General Partner” is defined in the preamble to this Agreement.

“MLP Omnibus Agreement” means that certain Omnibus Agreement, dated as of May 14, 2008, by and among Western Gas Partners, LP, Western Gas Holdings, LLC and Anadarko, as heretofore amended.

“Partnership” is defined in the preamble to this Agreement.

“Partnership Agreement” means the First Amended and Restated Agreement of Limited Partnership of the Partnership, dated as of the Closing Date, as such agreement is in effect on the Closing Date, to which reference is hereby made for all purposes of this Agreement.

“Partnership Entities” means the General Partner and each member of the Partnership Group.

“Partnership Group” means the Partnership and its Subsidiaries (other than Western Gas Partners, LP and its Subsidiaries) treated as a single consolidated entity.

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“Party” and “Parties” are defined in the preamble to this Agreement.

“Person” means an individual, corporation, partnership, joint venture, trust, limited liability company, unincorporated organization or any other entity.

“Subsidiary” means, with respect to any Person, (i) a corporation of which more than 50% of the voting power of shares entitled (without regard to the occurrence of any contingency) to vote in the election of directors or other governing body of such corporation is owned, directly or indirectly, at the date of determination, by such Person, by one or more Subsidiaries of such Person or a combination thereof, (ii) a partnership (whether general or limited) in which such Person or a Subsidiary of such Person is, at the date of determination, a general partner, but only if such Person, directly or indirectly through one or more Subsidiaries of such Person, or a combination thereof, controls such partnership on the date of determination, or (iii) any other Person (other than a corporation or a partnership) in which such Person, one or more Subsidiaries of such Person, or a combination thereof, directly or indirectly, at the date of determination, has (A) at least a majority ownership interest or (B) the power to elect or direct the election of a majority of the directors or other governing body of such Person.

“Voting Securities” means securities of any class of a Person entitling the holders thereof to vote in the election of, or to appoint, members of the board of directors or other similar governing body of the Person.

ARTICLE II

SERVICES

2.1 Provision of Services; Reimbursement and Administrative Fee.

(a) Anadarko hereby agrees to cause the Anadarko Entities to continue to provide the Partnership Entities with certain general and administrative services, such as legal, accounting, treasury, cash management, insurance, administrative and claims processing, risk management, health, safety and environmental, information technology, human resources, credit, payroll, internal audit, tax, marketing and midstream. These general and administrative services shall be substantially identical in nature and quality to the services of such type previously provided by the Anadarko Entities to Western Gas Partners, LP and its Subsidiaries pursuant to the MLP Omnibus Agreement.

(b) The Partnership Group hereby agrees to reimburse Anadarko for all cash expenses and expenditures that the Anadarko Entities incur or payments they make on behalf of the Partnership Entities for the general and administrative services provided for in Section 2.1(a).

(c) In addition to the reimbursement obligation described in Section 2.1(b), the Partnership shall pay Anadarko (or an Anadarko Entity designated by Anadarko) an administrative fee (the “Administrative Fee”) of $250,000 per year (subject to adjustment as specified below), payable in arrears in equal quarterly installments on or before the 30th day following the end of each fiscal quarter following the Closing Date (pro rated to account for any

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partial quarterly period). On January 1, 2014 and each January 1st thereafter, the Administrative Fee shall be increased by the percentage increase in the Consumer Price Index – All Urban Consumers, U.S. City Average, Not Seasonally Adjusted (the “CP Index”). In making such adjustment, the Administrative Fee shall be increased by the CP Index for the prior year period based on the most recent information available from the U.S. Department of Labor.

2.2 Reimbursement for Publicly Traded Partnership Expenses. The Partnership Entities hereby agree to reimburse Anadarko for all expenses and expenditures that the Anadarko Entities incur or payments that they make as a result of the Partnership’s becoming a publicly traded partnership, including (but not limited to) expenses associated with annual and quarterly reporting; tax return and Schedule K-1 preparation and distribution expenses; Sarbanes-Oxley compliance expenses; expenses associated with listing on the New York Stock Exchange; independent auditor fees; legal fees; investor relations expenses; and registrar and transfer agent fees. Furthermore, the Partnership Entities agree to reimburse Anadarko for any such expenses incurred on or before the Closing Date by the Anadarko Entities on behalf of the Partnership Entities.

2.3 Reimbursement for Insurance. The Partnership Entities hereby agree to reimburse Anadarko for all expenses that the Anadarko Entities incur or payments that they make on behalf of the Partnership Entities for insurance coverage with respect to the Partnership Assets.

2.4 Reimbursement Procedures. On or before the fifth business day of each month, Anadarko shall send an invoice to the General Partner for that amount of money associated with all expenses or expenditures incurred or payments made by the Anadarko Entities during the preceding month that are to be reimbursed by the Partnership Entities pursuant to Sections 2.1(b), 2.2 and 2.3 hereof. Where it is not reasonably practicable to determine the cost of such an expense, expenditure or payment, Anadarko or the applicable Anadarko Entity may make a good faith reasonable estimate of such expense, expenditure or payment (and provided that any such estimates, other than with respect to benefit load, are “trued up” within 10 days of the end of each quarter based on the actual amount of the expenses, expenditures or payments in respect of which estimates were made in the immediately preceding quarter). Subject to the parenthetical clause in the immediately preceding sentence, the Partnership Entities shall accept any estimate or benefit load described in this paragraph, provided that such estimate is reasonable and made in good faith. The Partnership Entities shall pay such invoice within 30 days of receipt.

ARTICLE III

MISCELLANEOUS

3.1 Accuracy of Recitals. The paragraphs contained in the recitals to this Agreement are incorporated in this Agreement by this reference, and the Parties to this Agreement acknowledge the accuracy thereof.

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3.2 Choice of Law; Submission to Jurisdiction. This Agreement shall be subject to and governed by the laws of the State of Texas. Each Party hereby submits to the jurisdiction of the state and federal courts in the State of Texas and to venue in Houston, Texas.

3.3 Notices. Any notice, demand, or communication required or permitted under this Agreement shall be in writing and delivered personally, by reputable courier, or by telecopier, and shall be deemed to have been duly given as of the date and time reflected on the delivery receipt if delivered personally or sent by reputable courier service, or on the automatic telecopier receipt if sent by telecopier, addressed as follows:

If to Anadarko:

Anadarko Petroleum Corporation

1201 Lake Robbins Drive

The Woodlands, Texas 77380

Attn: General Counsel

Fax: 832-636-3214

If to the Partnership or the General Partner:

Western Gas Equity Holdings, LLC

1201 Lake Robbins Drive

The Woodlands, Texas 77380

Attn: President

Fax: 832-636-6001

A Party may change its address for the purposes of notices hereunder by giving notice to the other Party specifying such changed address in the manner specified in this Section 3.3.

3.4 Further Assurances. The Parties agree to execute such additional instruments, agreements and documents, and to take such other actions, as may be necessary to effect the purposes of this Agreement.

3.5 Agreement. This Agreement constitutes the entire agreement of the Parties relating to the matters contained herein, superseding all prior contracts or agreements, whether oral or written, relating to the matters contained herein.

3.6 Termination. This Agreement shall terminate upon a Change of Control of the General Partner or the Partnership, other than any Change of Control of the General Partner or the Partnership that may be deemed to have occurred pursuant to clause (iv) of the definition of Change of Control solely as a result of a Change of Control of Anadarko. Notwithstanding any other provision of this Agreement, if the General Partner is removed as general partner of the Partnership under circumstances where Cause does not exist and Common Units held by the General Partner and its Affiliates are not voted in favor of such removal, this Agreement may immediately thereupon be terminated by Anadarko.

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3.7 Effect of Waiver or Consent. No waiver or consent, express or implied, by any Party to or of any breach or default by any Person in the performance by such Person of its obligations hereunder shall be deemed or construed to be a consent or waiver to or of any other breach or default in the performance by such Person of the same or any other obligations of such Person hereunder. Failure on the part of a Party to complain of any act of any Person or to declare any Person in default, irrespective of how long such failure continues, shall not constitute a waiver by such Party of its rights hereunder until the applicable statute of limitations period has run.

3.8 Amendment or Modification. This Agreement may be amended or modified from time to time only by the written agreement of all the Parties. Each such instrument shall be reduced to writing and shall be designated on its face an “Amendment” or an “Addendum” to this Agreement.

3.9 Assignment; Third-Party Beneficiaries. No Party shall have the right to assign its rights or obligations under this Agreement without the prior written consent of the other Parties. Each of the Parties hereto specifically intends that each entity comprising the Anadarko Entities and the Partnership Entities, as applicable, whether or not a Party to this Agreement, shall be entitled to assert rights and remedies hereunder as third-party beneficiaries hereto with respect to those provisions of this Agreement affording a right, benefit or privilege to any such entity.

3.10 Counterparts. This Agreement may be executed in any number of counterparts with the same effect as if all signatory Parties had signed the same document. All counterparts shall be construed together and shall constitute one and the same instrument.

3.11 Severability. If any provision of this Agreement or the application thereof to any Person or circumstance shall be held invalid or unenforceable to any extent, the remainder of this Agreement and the application of such provision to other Persons or circumstances shall not be affected thereby and shall be enforced to the greatest extent permitted by law.

3.12 Interpretation. In this Agreement, unless a clear contrary intention appears: (a) the singular includes the plural and vice versa; (b) reference to any Person includes such Person’s successors and assigns but, in the case of any Party, only if such successors and assigns are permitted by this Agreement, and reference to a Person in a particular capacity excludes such Person in any other capacity; (c) reference to any gender includes each other gender; (d) reference to any agreement (including this Agreement), document or instrument means such agreement, document, or instrument as amended or modified and in effect from time to time in accordance with the terms thereof and, if applicable, the terms of this Agreement; (e) reference to any Section means such Section of this Agreement, and references in any Section or definition to any clause means such clause of such Section or definition; (f) “hereunder,” “hereof,” “hereto” and words of similar import will be deemed references to this Agreement as a whole and not to any particular Section or other provision hereof or thereof; (g) “including” (and with correlative meaning “include”) means including without limiting the generality of any description preceding such term; and (h) relative to the determination of any period of time, “from” means “from and including,” “to” means “to but excluding” and “through” means “through and including.”

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3.13 Titles and Headings. Section titles and headings in this Agreement are inserted for convenience of reference only and are not intended to be a part of, or to affect the meaning or interpretation of, this Agreement.

3.14 Relationship of the Parties.

(a) Nothing in this Agreement shall cause any of the Anadarko Entities or the Partnership Entities to become members of any other partnership, joint venture, association, syndicate or other entity. Nothing in this Agreement shall cause any Partnership Entity to be considered an Anadarko Entity, and vice versa.

(b) For purposes of this Agreement, no Partnership Entity shall be deemed to be an Affiliate of the Anadarko Entities nor shall any Anadarko Entity be deemed to be an Affiliate of any the Partnership Entities.

3.15 Binding Effect. This Agreement will be binding upon, and will inure to the benefit of, the Parties and their respective successors, permitted assigns and legal representatives.

3.16 Time of the Essence. Time is of the essence in the performance of this Agreement.

3.17 Delay or Partial Exercise Not Waiver. No failure or delay on the part of any Party to exercise any right or remedy under this Agreement will operate as a waiver thereof; nor shall any single or partial exercise of any right or remedy under this Agreement preclude any other or further exercise thereof or the exercise of any other right or remedy granted hereby or any related document. The waiver by either Party of a breach of any provisions of this Agreement will not constitute a waiver of a similar breach in the future or of any other breach or nullify the effectiveness of such provision.

3.18 Withholding or Granting of Consent. Unless otherwise provided in this Agreement, each Party may, with respect to any consent or approval that it is entitled to grant pursuant to this Agreement, grant or withhold such consent or approval in its sole and uncontrolled discretion, with or without cause, and subject to such conditions as it shall deem appropriate.

3.19 Laws and Regulations. Notwithstanding any provision of this Agreement to the contrary, no Party shall be required to take any act, or fail to take any act, under this Agreement if the effect thereof would be to cause such Party to be in violation of any applicable law, statute, rule or regulation.

3.20 Negation of Rights of Limited Partners, Assignees and Third Parties. Except as set forth in Section 3.9, the provisions of this Agreement are enforceable solely by the Parties, and no limited partner, member, or assignee of Anadarko, the Partnership, the General Partner or other Person shall have the right, separate and apart from Anadarko, the Partnership or the General Partner, to enforce any provision of this Agreement or to compel any Party to comply with the terms of this Agreement.

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3.21 No Recourse Against Officers or Directors. For the avoidance of doubt, the provisions of this Agreement shall not give rise to any right of recourse against any officer or director of any Anadarko Entity or any Partnership Entity.

3.22 Signatories Duly Authorized. Each of the signatories to this Agreement represents that he is duly authorized to execute this Agreement on behalf of the Party for which he is signing, and that such signature is sufficient to bind the Party purportedly represented.

[Signature page follows]

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IN WITNESS WHEREOF, the Parties have executed this Agreement on, and effective as of, the Closing Date.

Signature Page–Omnibus Agreement of

Western Gas Equity Partners, LP