Exhibit 99.1

December 21, 2010

Webster Financial Corporation

Webster Plaza

145 Bank Street

Waterbury, Connecticut 06702

Ladies and Gentlemen:

Reference is hereby made to (i) the Investment Agreement, dated as of July 27, 2009 (the “Investment Agreement”), between Webster Financial Corporation, a Delaware corporation (the “Company”) and Warburg Pincus Private Equity X, L.P., a Delaware limited partnership (“WP Private Equity X”); (ii) the Letter Agreement, dated as of October 15, 2009, among the Company, WP Private Equity X and Warburg Pincus X Partners, L.P. (“WP X Partners,” and together with WP Private Equity X, “WP X”); (iii) the notice given by the Company to WP X, dated as of December 3, 2010, notifying WP X of its gross-up right under Section 4.3 of the Investment Agreement (the “Gross-up Right”) in connection with a proposed public offering (the “Offering”) by the Company of 6,630,000 shares of its common stock, par value $0.01 per share (“Common Stock”) for $18.00 per share of Common Stock (the “Offering Price”) payable on December 27, 2010; and (iv) the notice given by WP X, dated as of December 6, 2010, notifying the Company of WP X’s intention to exercise the Gross-up Right subject to the conditions set forth in such notice. Capitalized terms used but not otherwise defined herein shall have the respective meanings set forth in the Investment Agreement. This letter agreement (this “Letter Agreement”) confirms the mutual understanding and agreement of the parties hereto with respect to the exercise by WP X of the Gross-up Right.

1. Transaction and Purchase Price. Subject only to the consummation of the Offering and the provisions of Section 4.3 of the Investment Agreement (other than the first sentence of paragraph (c) thereof), WP X hereby agrees to purchase from the Company, and the Company agrees to issue and sell to WP X, an aggregate of 2,069,848 shares of Common Stock (the “Purchased Shares”) at a price per share equal to $17.605 (the Offering Price, less any underwriting discounts or sales commissions) allocated as follows: (a) WP Private Equity X —2,005,683 shares of Common Stock in exchange for $35,310,049.22; and (b) WP X

Partners — 64,165 shares of Common Stock in exchange for $1,129,624.83 (the sum of the amounts in clauses (a) and (b), the “Purchase Price”). The transactions contemplated by the preceding sentence will be consummated on December 27, 2010 (the “Closing Date”) substantially simultaneously with the closing of the Offering. WP X will pay the Purchase Price on the Closing Date by wire transfer of immediately available funds to an account designated by the Company at least one business day prior to the Closing Date. The Company will deliver on the Closing Date to WP X confirmations of book entry transfer evidencing the foregoing transactions. The Purchased Shares will bear only the first legend set forth in Section 4.5(a) of the Investment Agreement. In addition, WP X agrees not to exercise any “piggyback registration” rights set forth in Section 4.11(a)(4) of the Investment Agreement in connection with the Offering.

2. Representations and Warranties of the Company. Except as Previously Disclosed, the Company represents and warrants as of the date of this Letter Agreement (except to the extent made only as of a specified date, in which case as of such date) to WP X that:

(1) The Company has the corporate power and authority to enter into this Letter Agreement and to carry out its obligations hereunder. This Letter Agreement has been duly and validly executed and delivered by the Company and, assuming due authorization, execution and delivery of this Letter Agreement by WP X, are valid and binding obligations of the Company enforceable against the Company in accordance with their respective terms, except as such enforceability may be limited by bankruptcy, insolvency, moratorium, reorganizations, fraudulent transfer or similar laws relating to or affecting creditors generally or by general equitable principles (whether applied in equity or at law). No other corporate proceedings are necessary for the execution and delivery by the Company of this Letter Agreement, the performance by it of its obligations hereunder or the consummation by it of the transactions contemplated hereby.

(2) Neither the execution, delivery and performance by the Company of this Letter Agreement, nor the consummation of the transactions contemplated hereby, will (i) violate, conflict with, or result in a breach of any provision of, or constitute a default (or an event which, with notice or

2

lapse of time or both, would constitute a default) under, or result in the termination of, or accelerate the performance required by, or result in a right of termination or acceleration of, or result in the creation of, any Lien, upon any of the properties or assets of the Company or any Company Subsidiary under any of the material terms, conditions or provisions of (A) its certificate of incorporation or bylaws (or similar governing documents) or (B) any note, bond, mortgage, indenture, deed of trust, license, lease, agreement or other instrument or obligation to which the Company or any Company Subsidiary is a party or by which it may be bound, or to which the Company or any Company Subsidiary or any of the properties or assets of the Company or any Company Subsidiary may be subject, or (ii) subject to compliance with the statutes and regulations referred to in the next paragraph, violate any ordinance, permit, concession, grant, franchise, law, statute, rule or regulation or any judgment, ruling, order, writ, injunction or decree applicable to the Company or any Company Subsidiary or any of their respective properties or assets except in the case of clauses (i)(B) and (ii) for such violations, conflicts and breaches as would not reasonably be expected to have a Material Adverse Effect on the Company.

(3) Other than the securities or blue sky laws of the various states, no material notice to, registration, declaration or filing with, exemption or review by, or authorization, order, consent or approval of, any Governmental Entity, or expiration or termination of any statutory waiting period, is necessary for the consummation by the Company of the transactions set forth in this Letter Agreement.

3. Representations and Warranties of WP X. Except as Previously Disclosed, WP X hereby represents and warrants as of the date of this Letter Agreement (except to the extent made only as of a specified date, in which case as of such date) to the Company that:

3

(1) Each of WP Private Equity X and WP X Partners has the power and authority to enter into this Letter Agreement and to carry out its obligations hereunder. The execution, delivery and performance of this Letter Agreement by each of WP Private Equity X and WP X Partners and the consummation of the transactions contemplated hereby have been duly authorized by such party and no further approval or authorization is required. This Letter Agreement is a valid and binding obligation of each of WP Private Equity X and WP X Partners enforceable against it in accordance with its respective terms, except as such enforceability may be limited by bankruptcy, insolvency, moratorium, reorganizations, fraudulent transfer or similar laws affecting creditors generally or by general equitable principles (whether applied in equity or at law). No other proceedings are necessary for the execution and delivery by each of WP Private Equity X and WP X Partners of this Letter Agreement, the performance by it of its obligations hereunder or the consummation by it of the transactions contemplated hereby.

(2) Neither the execution, delivery and performance by each of WP Private Equity X and WP X Partners of this Letter Agreement, nor the consummation of the transactions contemplated hereby, nor compliance by such party with any of the provisions hereof, will (i) violate, conflict with, or result in a breach of any provision of, or constitute a default (or an event which, with notice or lapse of time or both, would constitute a default) under, or result in the termination of, or accelerate the performance required by, or result in a right of termination or acceleration of, or result in the creation of, any Lien upon any of the properties or assets of such party under any of the material terms, conditions or provisions of (A) its certificate of limited partnership, partnership agreement or similar organizational documents or (B) any note, bond, mortgage, indenture, deed of trust, license, lease, agreement or other instrument or obligation to which such party is a party or by which it may be bound, or to which such party or any of the properties or assets of such party may be subject, or (ii) subject to compliance with the statutes and regulations referred to in the next paragraph, violate any statute, rule or regulation or, to the knowledge of such party, any judgment, ruling, order, writ, injunction or decree applicable to such party or any of their respective properties or assets except in the case of clauses (i)(B) and (ii) for such violations, conflicts and breaches as would not reasonably be expected to have a Material Adverse Effect on such party.

4

(3) Other than the securities or blue sky laws of the various states, no material notice to, registration, declaration or filing with, exemption or review by, or authorization, order, consent or approval of, any Governmental Entity, or expiration or termination of any statutory waiting period, is necessary for the consummation by WP X of the transactions set forth in this Letter Agreement.

4. Survival. Each of the representations and warranties set forth in this Letter Agreement shall survive the closing indefinitely. Except as otherwise provided herein, all covenants and agreements contained herein shall survive for the duration of any statutes of limitations applicable thereto or until, by their respective terms, they are no longer operative.

5. Registrable Securities. The parties hereto agree that, for the avoidance of doubt, the definition of the term “Registrable Securities” under the Investment Agreement shall be deemed to include the Purchased Shares.

6. Amendment. No amendment or waiver of this Letter Agreement will be effective with respect to any party unless made in writing and signed by an officer of a duly authorized representative of such party.

7. Waivers. No failure or delay by any party in exercising any right, power or privilege hereunder shall operate as a waiver thereof nor shall any single or partial exercise thereof preclude any other or further exercise thereof or the exercise of any other right, power or privilege. No waiver of any party to this Letter Agreement will be effective unless it is in a writing signed by a duly authorized officer of the waiving party that makes express reference to the provision or provisions subject to such waiver.

8. Counterparts and Facsimile. For the convenience of the parties hereto, this Letter Agreement may be executed in any number of separate counterparts, each such counterpart being deemed to be an original instrument, and all such counterparts will together constitute the same agreement. Executed signature pages to this Letter Agreement may be delivered by facsimile or other comparable electronic means and as so delivered will be deemed as sufficient as if actual signature pages had been delivered.

9. GOVERNING LAW. THIS AGREEMENT WILL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK APPLICABLE TO CONTRACTS MADE AND TO BE PERFORMED ENTIRELY WITHIN SUCH STATE. THE PARTIES HEREBY IRREVOCABLY AND UNCONDITIONALLY CONSENT TO SUBMIT TO THE EXCLUSIVE JURISDICTION OF THE STATE AND FEDERAL COURTS LOCATED IN THE STATE OF NEW YORK FOR ANY ACTIONS, SUITS OR PROCEEDINGS ARISING OUT OF OR RELATING TO THIS AGREEMENT AND THE TRANSACTIONS CONTEMPLATED HEREBY.

10. WAIVER OF JURY TRIAL. EACH OF THE PARTIES HERETO HEREBY IRREVOCABLY WAIVES ANY AND ALL RIGHT TO TRIAL BY JURY IN

5

ANY LEGAL PROCEEDING ARISING OUT OF OR RELATED TO THIS AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY.

11. Notices. The provisions of Section 6.7 of the Investment Agreement are incorporated herein by reference as if set out in full herein.

12. Entire Agreement, Etc. (a) This Letter Agreement, together with Section 4.3 of the Investment Agreement, constitutes the entire agreement, and supersedes all other prior agreements, understandings, representations and warranties, both written and oral, between the parties, with respect to the subject matter hereof; (b) the terms and conditions of this Letter Agreement shall inure to the benefit of and be binding upon the parties hereto and their respective successors, and with respect to WP X, its permitted assigns; and (c) this Letter Agreement will not be assignable by operation of law or otherwise (any attempted assignment in contravention hereof being null and void), except that WP X shall be permitted to assign its rights or obligations hereunder to (i) any Affiliate entity, but only if the transferee agrees in writing for the benefit of the Company (with a copy thereof to be furnished to the Company (any such transferee shall be included in the term “WP”)); provided, further, that no such assignment shall relieve WP of any of its obligations under this Letter Agreement.

13. Severability. If any provision of this Letter Agreement or the application thereof to any person (including, the officers and directors of WP X and the Company) or circumstance is determined by a court of competent jurisdiction to be invalid, void or unenforceable, the remaining provisions hereof, or the application of such provision to persons or circumstances other than those as to which it has been held invalid or unenforceable, will remain in full force and effect and shall in no way be affected, impaired or invalidated thereby, so long as the economic or legal substance of the transactions contemplated hereby is not affected in any manner materially adverse to any party. Upon such determination, the parties shall negotiate in good faith in an effort to agree upon a suitable and equitable substitute provision to effect the original intent of the parties.

14. No Third Party Beneficiaries. Nothing contained in this Letter Agreement, expressed or implied, is intended to confer upon any person other than the parties hereto, any benefit right or remedies.

[Signature page follows]

6

If the foregoing accurately reflects your understanding and agreement, please acknowledge the same by signing this Letter Agreement where indicated below and returning to us a copy of this letter.