Exhibit 5.1

March 30, 2020

The TJX Companies, Inc.

770 Cochituate Road

Framingham, MA 01701

Re: Registration Statement on Form S-3 (Registration No. 333-237461)

Ladies and Gentlemen:

We have acted as counsel to The TJX Companies, Inc., a Delaware corporation (the “Company”), in connection with the issuance and sale of (a) $1,250,000,000 aggregate principal amount of 3.500% notes due 2025 of the Company (the “2025 Notes”), (b) $750,000,000 aggregate principal amount of 3.750% notes due 2027 of the Company (the “2027 Notes”), (c) $1,250,000,000 aggregate principal amount of 3.875% notes due 2030 of the Company (the “2030 Notes”) and (d) $750,000,000 aggregate principal amount of 4.500% notes due 2050 of the Company (the “2050 Notes” and, together with the 2025 Notes, 2027 Notes and the 2030 Notes, the “Notes”) pursuant to the above-referenced automatically effective shelf registration statement (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), on March 30, 2020 by the Company. The Notes are being issued under an Indenture (the “Base Indenture”), as supplemented by a First Supplemental Indenture relating to the 2025 Notes (the “First Supplemental Indenture”), a Second Supplemental Indenture relating to the 2027 Notes (the “Second Supplemental Indenture”), a Third Supplemental Indenture relating to the 2030 Notes (the “Third Supplemental Indenture”) and a Fourth Supplemental Indenture relating to the 2050 Notes (the “Fourth Supplemental Indenture”), and collectively with the Base Indenture, the First Supplemental Indenture, the Second Supplemental Indenture and the Third Supplemental Indenture, the “Indenture”), that will be executed by and between the Company and U.S. Bank National Association, as trustee (the “Trustee”), on the closing date of the offering of the Notes.

In connection with this opinion letter, we have examined the Registration Statement and the Base Indenture, the form of which has been filed with the Commission as an exhibit to the Registration Statement, the First Supplemental Indenture, the Second Supplemental Indenture, the Third Supplemental Indenture and the Fourth Supplemental Indenture. We have also examined such certificates, documents and records and have made such investigation of fact and

such examination of law as we have deemed appropriate in order to enable us to render the opinions set forth herein. In conducting such investigation, we have relied, without independent verification, upon certificates of officers of the Company, public officials and other appropriate persons.

The opinions expressed below are limited to the laws of the State of New York and the Delaware General Corporation Law.

Based upon and subject to the foregoing and the qualifications and limitations set forth below, we are of the opinion that, when the Base Indenture, the First Supplemental Indenture, the Second Supplemental Indenture, the Third Supplemental Indenture and the Fourth Supplemental Indenture have been duly executed and delivered by the Company and the Trustee, and the Notes have been duly executed and authenticated in accordance with the provisions of the Indenture and have been delivered against receipt of payment therefor, the Notes will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

Our opinions set forth above are subject to (a) bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance and similar laws affecting the rights and remedies of creditors generally and (b) general principles of equity. Our opinions are also subject to the qualification that the enforceability of provisions in the Indenture and the Notes providing for indemnification or contribution, broadly worded waivers, waivers of rights to damages or defenses, waivers of unknown or future claims, and waivers of statutory, regulatory or constitutional rights may be limited on public policy or statutory grounds. In addition, we express no opinion with respect to the enforceability of rights to receive prepayment premiums or the unaccrued portion of original issue discount upon acceleration of the Notes, in each case to the extent determined to be unreasonable or to constitute unmatured interest.

We hereby consent to the incorporation by reference of this opinion letter as an exhibit to the Registration Statement and to the use of our name (a) under the caption “Validity of Debt Securities” in the Registration Statement and (b) under the caption “Legal Matters” in the prospectus supplement relating to the Notes. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

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