Exhibit 5.1

May 11, 2020

Digital Realty Trust, Inc.

Four Embarcadero Center, Suite 3200

San Francisco, California 94111

Ladies and Gentlemen:

We have served as Maryland counsel to Digital Realty Trust, Inc., a Maryland corporation (the “Company”), in connection with certain matters of Maryland law arising out of the sale and issuance from time to time of shares (the “Shares”) of common stock, $.01 par value per share (the “Common Stock”), of the Company having an aggregate offering price of up to $1,000,000,000 (the “Offering”), covered by the above-referenced Registration Statement, and all amendments thereto (the “Registration Statement”), filed by the Company and Digital Realty Trust, L.P., a Maryland limited partnership (the “Operating Partnership”), with the United States Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “1933 Act”). The Shares are to be issued pursuant to an ATM Equity Offering Sales Agreement, dated January 4, 2019, as amended by Amendment No. 1 to ATM Equity Offering Sales Agreement, dated as of March 17, 2020, and as further amended by Amendment No. 2 to ATM Equity Offering Sales Agreement, dated as of May 11, 2020 (as amended, the “Sales Agreement”), by and among the Company, the Operating Partnership, each of the entities named therein as a sales agent, forward seller and/or principal and each of the entities named therein as a forward purchaser.

In connection with our representation of the Company, and as a basis for the opinion hereinafter set forth, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the following documents (hereinafter collectively referred to as the “Documents”):

1. The Registration Statement;

2. The Prospectus, dated March 17, 2020, as supplemented by a Prospectus Supplement, dated May 11, 2020, filed with the Commission pursuant to Rule 424(b)(2) of the General Rules and Regulations promulgated under the 1933 Act;

3. The charter of the Company (the “Charter”), certified by the State Department of Assessments and Taxation of Maryland (the “SDAT”);

4. The Eighth Amended and Restated Bylaws of the Company (the “Bylaws”), certified as of the date hereof by an officer of the Company;

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May 11, 2020

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5. A certificate of the SDAT as to the good standing of the Company, dated as of a recent date;

6. Resolutions (the “Resolutions”) adopted by the Board of Directors of the Company (the “Board”) relating to, among other matters, (a) the authorization of the sale and issuance of the Shares and (b) the delegation to certain officers of the Company (the “Authorized Officers”) of the power to determine, subject to certain parameters, the number of Shares and the offering price of each Share to be sold from time to time pursuant to the Sales Agreement and any related Terms Agreement or Confirmation (each as defined in the Sales Agreement), certified as of the date hereof by an officer of the Company;

7. The Sales Agreement;

8. A certificate executed by an officer of the Company, dated as of the date hereof; and

9. Such other documents and matters as we have deemed necessary or appropriate to express the opinion set forth below, subject to the assumptions, limitations and qualifications stated herein.

In expressing the opinion set forth below, we have assumed the following:

1. Each individual executing any of the Documents, whether on behalf of such individual or any other person, is legally competent to do so.

2. Each individual executing any of the Documents on behalf of a party (other than the Company) is duly authorized to do so.

3. Each of the parties (other than the Company) executing any of the Documents has duly and validly executed and delivered each of the Documents to which such party is a signatory, and such party’s obligations set forth therein are legal, valid and binding and are enforceable in accordance with all stated terms.

4. All Documents submitted to us as originals are authentic. The form and content of all Documents submitted to us as unexecuted drafts do not differ in any respect relevant to this opinion from the form and content of such Documents as executed and delivered. All Documents submitted to us as certified or photostatic copies conform to the original documents. All signatures on all Documents are genuine. All public records reviewed or relied upon by us or on our behalf are true and complete. All representations, warranties, statements and information contained in the Documents are true and complete. There has been no oral or written modification of or amendment to any of the Documents, and there has been no waiver of any provision of any of the Documents, by action or omission of the parties or otherwise.

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5. The Shares will not be issued or transferred in violation of the restrictions on transfer and ownership set forth in Article VI of the Charter.

6. Upon the issuance of any of the Shares, the total number of shares of Common Stock issued and outstanding will not exceed the total number of shares of Common Stock that the Company is then authorized to issue under the Charter.

7. The number of Shares, and the offering price of each Share, to be issued by the Company from time to time pursuant to the Sales Agreement and any related Terms Agreement or Confirmation will be authorized and approved by the Board or the Authorized Officers in accordance with the Maryland General Corporation Law, the Charter, the Bylaws and the Resolutions (with such approvals referred to hereinafter as the “Corporate Proceedings”) prior to the issuance thereof.

Based upon the foregoing, and subject to the assumptions, limitations and qualifications stated herein, it is our opinion that:

1. The Company is a corporation duly incorporated and existing under and by virtue of the laws of the State of Maryland and is in good standing with the SDAT.

2. The issuance of the Shares has been duly authorized and, when and to the extent issued against payment therefor in accordance with the Sales Agreement and any related Terms Agreement or Confirmation, the Resolutions and the Corporate Proceedings, the Shares will be validly issued, fully paid and nonassessable.

The foregoing opinion is limited to the laws of the State of Maryland and we do not express any opinion herein concerning federal law or the laws of any other state. We express no opinion as to compliance with any federal or state securities laws, including the securities laws of the State of Maryland, or as to federal or state laws regarding fraudulent transfers. To the extent that any matter as to which our opinion is expressed herein would be governed by the laws of any jurisdiction other than the State of Maryland, we do not express any opinion on such matter. The opinion expressed herein is subject to the effect of judicial decisions which may permit the introduction of parol evidence to modify the terms or the interpretation of agreements.

The opinion expressed herein is limited to the matters specifically set forth herein and no other opinion shall be inferred beyond the matters expressly stated. We assume no obligation to supplement this opinion if any applicable law changes after the date hereof or if we become aware of any fact that might change the opinion expressed herein after the date hereof.

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May 11, 2020

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This opinion is being furnished to you for submission to the Commission as an exhibit to the Company’s Current Report on Form 8-K relating to the Offering (the “Current Report”), which is incorporated by reference in the Registration Statement. We hereby consent to the filing of this opinion as an exhibit to the Current Report and the said incorporation by reference and to the use of the name of our firm therein. In giving this consent, we do not admit that we are within the category of persons whose consent is required by Section 7 of the 1933 Act.

Very truly yours,

/s/ Venable LLP