Exhibit 5.1

[LETTERHEAD OF VENABLE LLP]

September 27, 2018

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 registration of up to 9,775,000 shares of common stock, $.01 par value per share (the “Common Stock”), of the Company, including up to 1,275,000 shares of Common Stock (the “Option Shares”) which the Underwriters (as defined herein) have the option to purchase, 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”). Pursuant to the Underwriting Agreement, dated September 24, 2018 (the “Underwriting Agreement”), by and among the Company, the Operating Partnership, Merrill Lynch, Pierce, Fenner & Smith Incorporated and Citigroup Global Markets Inc., as representatives of the several underwriters named in Schedule II thereto (collectively, the “Underwriters”), Bank of America, N.A. and Citigroup Global Markets Inc., as forward sellers (collectively, the “Forward Sellers”), and Bank of America, N.A. and Citibank, N.A., as forward purchasers (collectively, the “Forward Purchasers”), the Forward Sellers will borrow from third parties and sell to the Underwriters up to 9,775,000 shares of Common Stock (the “Borrowed Shares”), including up to 1,275,000 Option Shares. If the Forward Sellers do not borrow from third parties and sell to the Underwriters the total number of shares of Common Stock required to be borrowed and sold pursuant to the Forward Sale Agreements (as defined herein), the Company will issue and sell to the Underwriters an aggregate number of shares of Common Stock equal to the number of Borrowed Shares that the Forward Sellers do not borrow from third parties and sell to the Underwriters (the “Company Shares”).

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;

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September 27, 2018

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2.    The Prospectus, dated September 22, 2017, as supplemented by a Prospectus Supplement, dated September 24, 2018 (the “Prospectus Supplement”), 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 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;

6.    Resolutions adopted by the Board of Directors of the Company and a duly authorized committee thereof relating to, among other matters, the authorization of (a) the sale and issuance of the Company Shares, (b) the issuance to the Forward Purchasers on one or more dates no later than September 27, 2019 of a number of shares of Common Stock up to the aggregate of the maximum Share Caps (as such term is defined in the Forward Sale Agreements) in exchange for any consideration required to be paid by the Forward Purchasers pursuant to the terms of the Forward Sale Agreements (the “Settlement Shares” and, together with the Company Shares, the “Shares”) and (c) the registration of the Shares (the “Resolutions”), certified as of the date hereof by an officer of the Company;

7.    The Underwriting Agreement;

8.    The letter agreements, each dated September 24, 2018 (collectively, the “Forward Sale Agreements”), between the Company and each of the Forward Purchasers;

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

10.    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.

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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.

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 Settlement 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.

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 Company Shares has been duly authorized and, when and to the extent issued against payment therefor in accordance with the Registration Statement, the Prospectus Supplement, the Resolutions and the Underwriting Agreement, the Company Shares will be validly issued, fully paid and nonassessable.

3.    The issuance of the Settlement Shares has been duly authorized and, when and to the extent issued against payment therefor in accordance with the Registration Statement, the Prospectus Supplement, the Resolutions and the Forward Sale Agreements, the Settlement Shares will be validly issued, fully paid and nonassessable.

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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. 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 offering described in the Prospectus Supplement (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.