Exhibit 5.5

May 11, 2016

The Travelers Companies, Inc.

485 Lexington Avenue

New York, New York 10017

Ladies and Gentlemen:

We have acted as counsel to The Travelers Companies, Inc., a Minnesota corporation (the “Company”), in connection with the issuance of $500,000,000 aggregate principal amount of 3.750% Senior Notes due 2046 (the “Notes”) issued by the Company pursuant to the Underwriting Agreement, dated May 4, 2016 (the “Underwriting Agreement”), between the Company and the Underwriters named on Schedule 1 to the Underwriting Agreement (the “Underwriters”).

We have examined the Registration Statement on Form S-3 (File No. 333-189434) (the “Registration Statement”) filed by the Company under the Securities Act of 1933, as amended (the “Securities Act”), as it became effective under the Securities Act; the Company’s prospectus dated June 19, 2013 (the “Base Prospectus”), as supplemented by the prospectus supplement dated May 4, 2016 (the “Prospectus Supplement” and, together with the Base Prospectus, the “Prospectus”), filed by the Company pursuant to Rule 424(b) of the rules and regulations of the Securities and Exchange Commission (the “Commission”) under the Securities Act; the Indenture dated as of March 12, 2002 (the “Indenture”) between the Company and The Bank of New York Mellon Trust Company, N.A. (as successor to JPMorgan Chase Bank), as trustee (the “Trustee”), relating to the Notes, which has been filed as an exhibit to the Registration

Statement; the global notes representing the Notes; and the Underwriting Agreement. In addition, we have examined, and have relied as to matters of fact upon originals, or duplicates or certified or conformed copies, of such records, agreements, documents and other instruments and such certificates or comparable documents of public officials and of officers and representatives of the Company and have made such other investigations, as we have deemed relevant and necessary in connection with the opinions hereinafter set forth.

In rendering the opinions set forth below, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies and the authenticity of the originals of such latter documents. We also have assumed that the Indenture is the valid and legally binding obligation of the Trustee.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that the Notes have been duly authorized, executed and issued by the Company and, assuming due authentication thereof by the Trustee and upon payment and delivery in accordance with the provisions of the Indenture and the Underwriting Agreement, will constitute valid and legally binding obligations of the Company enforceable against the Company in accordance with their terms and entitled to the benefits of the Indenture.

Our opinion set forth above is subject to (i) the effects of bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally, (ii) general equitable principles (whether considered in a proceeding in equity or at law) and (iii) an implied covenant of good faith and fair dealing.

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Insofar as the opinions expressed herein relate to or are dependent upon matters governed by the law of the State of Minnesota, we have relied upon the opinion letter, dated the date hereof, of Wendy C. Skjerven, Esq., Vice President, Corporate Secretary and Group General Counsel of the Company.

We do not express any opinion herein concerning any law other than the law of the State of New York and, to the extent set forth herein, the law of the State of Minnesota.

We hereby consent to the filing of this opinion letter as Exhibit 5.5 to the Current Report on Form 8-K of the Company filed with the Commission in connection with the offer and sale of the Notes by the Company and to the use of our name under the captions “Legal Matters” in the Prospectus Supplement and “Material United States Federal Income Tax Consequences” in the Base Prospectus.

Very truly yours,

/s/ Simpson Thacher & Bartlett LLP

SIMPSON THACHER & BARTLETT LLP

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