Exhibit 5.1

September 19, 2013

Burlington Stores, Inc.

1830 Route 130 North

Burlington, New Jersey 08016

Ladies and Gentlemen:

We are acting as special counsel to Burlington Stores, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of a Registration Statement on Form S-1, originally filed with the Securities and Exchange Commission (the “Commission”) on June 27, 2013 (File No. 333-189632), under the Securities Act of 1933, as amended (the “Act”) (such Registration Statement, as amended or supplemented, is hereinafter referred to as the “Registration Statement”), relating to the proposed registration by the Company of up to 15,333,333 shares of common stock, par value $0.0001 per share, of the Company (“Common Stock”), including 2,000,000 shares of Common Stock to cover overallotments, if any. The shares of Common Stock to be sold by the Company identified in the Registration Statement are referred to herein as the “Shares” and the issuance of the Shares is referred to herein as the “Issuance.”

In that connection, we have examined originals, or copies certified or otherwise identified to our satisfaction, of such documents, corporate records and other instruments as we have deemed necessary for the purposes of this opinion, including (i) the Amended and Restated Certificate of Incorporation (the “Restated Charter”) of the Company in the form filed as Exhibit 3.1 to the Registration Statement, filed with the Commission on September 10, 2013 to be filed with the Secretary of State of the State of Delaware prior to the sale of the Shares; (ii) the Amended and Restated By-laws (the “By-laws”) of the Company in the form filed as Exhibit 3.2 to the Registration Statement, filed with the Commission on September 10, 2013; (iii) the form of Underwriting Agreement in the form filed as Exhibit 1.1 to the Registration Statement (the “Underwriting Agreement”), filed with the Commission on September 10, 2013; (iv) resolutions of the board of directors and stockholders of the Company with respect to the Issuance (the “Resolutions”); and (v) the Registration Statement.

For purposes of this opinion, we have assumed the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as copies and the authenticity of the originals of all documents submitted to us as copies. We have also assumed the legal capacity of all natural persons, the genuineness of the signatures of persons signing all documents in connection with which this opinion is rendered, the authority of such persons signing on behalf of the parties thereto (other than the Company) and the due authorization, execution and delivery of all documents by the parties thereto other than the Company. We have not

independently established or verified any facts relevant to the opinion expressed herein, but have relied upon statements and representations of officers and other representatives of the Company and others as to factual matters.

Based upon and subject to the foregoing qualifications, assumptions and limitations and the further limitations set forth below, we are of the opinion that, when (i) the Restated Charter is filed with the Secretary of State of the State of Delaware and (ii) the Registration Statement becomes effective under the Act, the Shares will be duly authorized and validly issued, fully paid and nonassessable.

Our opinions expressed above are subject to the qualifications that we express no opinion as to the applicability of, compliance with, or effect of any laws except the General Corporation Law of the State of Delaware.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our firm under the heading “Legal Matters” in the Registration Statement. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission.

We do not find it necessary for the purposes of this opinion, and accordingly we do not purport to cover herein, the application of the securities or “Blue Sky” laws of the various states to the Issuance.

This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. We assume no obligation to revise or supplement this opinion should the General Corporation Law of the State of Delaware be changed by legislative action, judicial decision or otherwise.

This opinion is furnished to you in connection with the filing of the Registration Statement, and is not to be used, circulated, quoted or otherwise relied upon for any other purposes.

Sincerely,

/s/ KIRKLAND & ELLIS LLP

KIRKLAND & ELLIS LLP