Blackstone Mortgage Trust (BXMT) 8-K Amendments to Articles of Incorporation or Bylaws

Exhibit 5.1

June 11, 2020

Blackstone Mortgage Trust, Inc.

345 Park Avenue, 42nd Floor

New York, New York 10154

Re:Registration Statement on FormS-3 (File No. 333-232852)

Ladies and Gentlemen:

We have served as Maryland counsel to Blackstone Mortgage Trust, Inc., a Maryland corporation (the “Company”), in connection with certain matters of Maryland law relating to the registration and issuance by the Company of up to 11,500,000 shares (the “Shares”) of class A common stock, par value $0.01 per share, of the Company (including up to 1,500,000 Shares issuable pursuant to an option granted to the underwriters in the offering to purchase additional Shares), in an underwritten public offering covered by the above-referenced Registration Statement, and all amendments thereto (collectively, the “Registration Statement”), filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”).

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 and the prospectus included therein in the form in which it was transmitted to the Commission under the Securities Act;

2. The Prospectus Supplement, dated June 8, 2020, in the form in which it was transmitted to the Commission under the Securities Act;

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

4. The Fifth 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 sale and issuance of the Shares (the “Resolutions”), certified as of the date hereof by an officer of the Company;

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

Blackstone Mortgage Trust, Inc.

June 11, 2020

Page 2

8. 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 another 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.

5. The Shares will not be issued or transferred in violation of the restrictions on transfer and ownership contained in Article VII of 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 validly 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 issued and delivered by the Company in accordance with the Resolutions and the Registration Statement against payment of the consideration set forth therein, the Shares will be validly issued, fully paid and nonassessable.

Blackstone Mortgage Trust, Inc.

June 11, 2020

Page 3

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 any judicial decision 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 Form8-K relating to the Shares (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 Securities Act.

Very truly yours,

/s/ Venable LLP