Exhibit 5.1

Hogan Lovells US LLP Columbia Square 555 Thirteenth Street, NW Washington, DC 20004 T +1 202 637 5600 F +1 202 637 5910 www.hoganlovells.com

May 11, 2020

Board of Directors

QTS Realty Trust, Inc.

12851 Foster Street

Overland Park, KS 66213

Ladies and Gentlemen:

We are acting as counsel to QTS Realty Trust, Inc., a Maryland corporation (the “Company”), in connection with the public offering of up to $500,000,000 aggregate gross sales price of the Company’s Class A common stock, $0.01 par value per share (the “Shares”), all of which are to be offered and sold by the Company from time to time pursuant to the terms of the Equity Distribution Agreement, dated May 11, 2020, by and among the Company, QualityTech, LP, a Delaware limited partnership (the “Operating Partnership”), and each of the persons named on Schedule 1 attached hereto (the “Equity Distribution Agreement”), which, among other things, contemplates that the Company may from time to time enter into one or more letter agreements with each of the persons named on Schedule 2 attached hereto (the “Forward Sale Agreements,” and together with the Equity Distribution Agreement, the “Agreements”), the form of which is attached as Schedule D of the Equity Distribution Agreement. The offering of the Shares by the Company is being made pursuant to a prospectus supplement dated May 11, 2020 and the accompanying base prospectus dated April 17, 2019 (such documents, collectively, the “Prospectus”) that form part of the Company’s effective registration statement on Form S-3 (File No. 333-230923) (the “Registration Statement”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinion hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including pdfs). We also have assumed that the Shares will not be issued in violation of the ownership limit contained in the Company’s Articles of Amendment and Restatement. As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

Hogan Lovells US LLP is a limited liability partnership registered in the District of Columbia. “Hogan Lovells” is an international legal practice that includes Hogan Lovells US LLP and Hogan Lovells International LLP, with offices in: Alicante Amsterdam Baltimore Beijing Birmingham Boston Brussels Colorado Springs Denver Dubai Dusseldorf Frankfurt Hamburg Hanoi Ho Chi Minh City Hong Kong Houston Johannesburg London Los Angeles Luxembourg Madrid Mexico City Miami Milan Minneapolis Monterrey Moscow Munich New York Northern Virginia Paris Perth Philadelphia Rome San Francisco São Paulo Shanghai Silicon Valley Singapore Sydney Tokyo Warsaw Washington, D.C. Associated Offices: Budapest Jakarta Riyadh Shanghai FTZ Ulaanbaatar Zagreb. Business Service Centers: Johannesburg Louisville. Legal Services Center: Berlin. For more information see www.hoganlovells.com

This opinion letter is based as to matters of law solely on the applicable provisions of Maryland General Corporation Law, as amended. We express no opinion herein as to any other statutes, rules or regulations.

Based upon, subject to and limited by the foregoing, we are of the opinion that following (i) execution and delivery by the Company and the Operating Partnership of the Equity Distribution Agreement, (ii) execution and delivery by the Company of each Forward Sale Agreement relating to any forward purchase pursuant to the Equity Distribution Agreement in the form attached as Schedule D to the Equity Distribution Agreement, together with the relevant supplemental confirmation thereto (the “Supplemental Confirmation”), (ii) authorization by the Company’s Board of Directors, or authorization by a duly authorized pricing committee thereof, within the limitations established by resolutions duly adopted by the Company’s Board of Directors and duly authorized pricing committee thereof, of the terms pursuant to which the Shares may be sold pursuant to the Agreements, (iii) authorization by a duly authorized executive officer, designated by the pricing committee to approve placement notices under the Agreements, of the terms of each placement notice issued and Supplemental Confirmation (if any) executed in a manner consistent with the foregoing and pursuant to which the Shares may be sold pursuant to the Agreements, (iv) issuance of the Shares pursuant to the terms established by the Board of Directors and the pricing committee thereof and the terms of the applicable Agreement and the applicable placement notice and Supplemental Confirmation (if any), and (vii) receipt by the Company of the proceeds for the Shares sold pursuant to the terms of such applicable Agreement and applicable placement notice and Supplemental Confirmation (if any), the Shares will be validly issued, fully paid and nonassessable.

This opinion letter has been prepared for use in connection with the filing by the Company of a Current Report on Form 8-K on the date hereof relating to the offer and sale of the Shares, which Form 8-K will be incorporated by reference into the Registration Statement and Prospectus, and speaks as of the date hereof. We assume no obligation to advise of any changes in the foregoing subsequent to the delivery of this letter.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the above-described Form 8-K and to the reference to this firm under the caption “Legal Matters” in the Prospectus. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Securities Act of 1933, as amended.

Very truly yours,

/s/ Hogan Lovells US LLP

HOGAN LOVELLS US LLP

Schedule 1

Schedule 2

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127 Public Square, 4th Floor

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Bank of Montreal

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Toronto, Ontario MAW 1AF

Bank of America, N.A.

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New York, New York 10036

Deutsche Bank AG, London Branch

Winchester House

1 Great Winchester St, London EC2N 2DB

Goldman Sachs & Co. LLC

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Jefferies LLC

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JPMorgan Chase Bank, National Association

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Mizuho Markets Americas LLC

c/o Mizuho Securities USA LLC, as agent
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Morgan Stanley & Co. LLC

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Royal Bank of Canada

c/o RBC Capital Markets, LLC

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The Toronto-Dominion Bank

TD Bank Tower

Toronto-Dominion Centre

Toronto, Ontario, M5K 1A2, Canada