Exhibit 5.1

[LETTERHEAD OF VENABLE LLP]

June 21, 2018

Digital Realty Trust, Inc.

Digital Realty Trust, L.P.

Suite 3200

Four Embarcadero Center

San Francisco, California 94111

Re: Registration Statement on Form S-3 (Registration Nos. 333-220576 and 333-220576-01)

Ladies and Gentlemen:

We have served as Maryland counsel to Digital Realty Trust, Inc., a Maryland corporation (the “Company”), and Digital Realty Trust, L.P., a Maryland limited partnership (the “Operating Partnership”), in connection with certain matters of Maryland law arising out of the registration of $650,000,000 aggregate principal amount of the Operating Partnership’s 4.450% Notes due 2028 (the “Notes”), and the guarantee by the Company of the obligations of the Operating Partnership under the Notes (the “Guarantee”). The Notes and the Guarantees are covered by the above-referenced Registration Statement, and all amendments thereto (the “Registration Statement”), filed by the Company and the Operating Partnership with the United States Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “1933 Act”).

In connection with our representation of the Company and the Operating Partnership, 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 September 22, 2017, as supplemented by a Prospectus Supplement, dated June 14, 2018, 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, certified by the State Department of Assessments and Taxation of Maryland (the “SDAT”);

4. The Seventh Amended and Restated Bylaws of the Company, certified as of the date hereof by an officer of the Company;

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

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Digital Realty Trust, L.P.

June 21, 2018

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6. The Certificate of Limited Partnership of the Operating Partnership, certified by the SDAT;

7. The Sixteenth Amended and Restated Agreement of Limited Partnership of the Operating Partnership, certified as of the date hereof by an officer of the Company;

8. A certificate of the SDAT as to the good standing of the Operating Partnership, dated as of a recent date;

9. Resolutions adopted by the Board of Directors of the Company, in its own capacity and in its capacity as the sole general partner of the Operating Partnership, or by a duly authorized committee thereof, relating to, among other matters, (a) the sale and issuance of the Notes, (b) the Guarantees and (c) the authorization of the execution, delivery and performance by the Company and the Operating Partnership of the Indenture (as defined herein), certified as of the date hereof by an officer of the Company;

10. The Indenture, dated as of June 23, 2015 (the “Base Indenture”), by and among the Operating Partnership, the Company and Wells Fargo Bank, National Association (the “Trustee”);

11. Supplemental Indenture No. 3, dated as of the date hereof (the “Supplemental Indenture” and, together with the Base Indenture, the “Indenture”), by and among the Operating Partnership, the Company and the Trustee;

12. The Guarantee contained in the Indenture;

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

14. 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.

Digital Realty Trust, Inc.

Digital Realty Trust, L.P.

June 21, 2018

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

3. Each of the parties (other than the Company or the Operating Partnership) 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.

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. The Operating Partnership is a limited partnership duly formed and existing under and by virtue of the laws of the State of Maryland and is in good standing with the SDAT.

2. The execution, delivery and performance of the Indenture have been duly authorized by all necessary corporate action of the Company and all necessary limited partnership action of the Operating Partnership. The Notes have been duly authorized for issuance by the Operating Partnership. The Guarantee has been duly authorized by the Company.

3. The Indenture has been duly executed and delivered by the Company and the Operating Partnership.

The foregoing opinion is limited to the laws of the State of Maryland and we do not express any opinion herein concerning any other law. 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 or the laws, codes or

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June 21, 2018

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regulations of any municipality or other local jurisdiction. 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.

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 Notes and the Guarantees (the “Current Report”), which is incorporated by reference in the Registration Statement. Latham & Watkins LLP, counsel to the Company and the Operating Partnership, may rely on this opinion in connection with any opinions to be delivered by it in connection with the Notes and the Guarantees. 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.