Exhibit 5.1

1735 Market Street, 51st Floor

Philadelphia, PA 19103-7599

TEL 215.665.8500

FAX 215.864.8999

www.ballardspahr.com

April 28, 2017

TransEnterix, Inc.

635 Davis Drive, Suite 300

Morrisville, NC 27560

Re: TransEnterix, Inc.

Ladies and Gentlemen:

We have acted as counsel to TransEnterix, Inc., a Delaware corporation (the “Company”) and are rendering this opinion in connection with a prospectus supplement, dated April 28, 2017 (the “Prospectus Supplement”), relating to the Registration Statement on Form S-3 (File No. 333-199998) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”) on November 7, 2014 and declared effective on December 19, 2014, and post-effectively amended pursuant to Post-Effective Amendment No. 1 on Form S-3, as filed with the SEC on March 8, 2016 and declared effective on June 22, 2016 (the “Prior Registration Statement”) and the related registration statement (File No. 333-217524) filed pursuant to Rule 462(b) under the Securities Act on April 28, 2017 (the “Related Registration Statement,” and together with the Prior Registration Statement, the “Registration Statement”) with respect to 24,900,000 units (the “Units”) consisting of one share of the Company’s common stock, par value $0.001 per share (the “Common Stock”), one Series A warrant to purchase one share of Common Stock (the “Series A Warrants”), and one Series B warrant to purchase 0.75 shares of Common Stock (the “Series B Warrants,” and together with the Series A Warrants, the “Warrants”). The Units, the shares of Common Stock underlying the Units (the “Shares”), the Warrants, and the shares of Common Stock underlying the Warrants (the “Warrant Shares”) are collectively referred to as the “Securities.”

The Securities are to be sold by the Company pursuant to an Underwriting Agreement dated April 28, 2017 (the “Agreement”) entered into by and between the Company and Stifel Nicolaus & Company, Incorporated (the “Underwriter”), which has been filed as Exhibit 1.1 to the Company’s Current Report on Form 8-K to which this opinion is attached as Exhibit 5.1.

We have examined originals or copies, certified or otherwise identified to our satisfaction, of (i) the Registration Statement and all exhibits thereto, (ii) the Prospectus Supplement, (iii) the Agreement, (iv) the forms of the Warrants, (v) the Amended and Restated Certificate of Incorporation of the Company together with all amendments thereto, (vi) the Amended and Restated Bylaws of the Company and (vii) certain resolutions of the Board of Directors of the Company and the Pricing Committee of the Board of Directors of the Company. We have also examined such corporate records and other agreements, documents and instruments, and such certificates or comparable documents of public officials and officers and representatives of the Company, and have made such inquiries of such officers and representatives and have considered such matters of law as we have deemed appropriate as the basis for the opinions hereinafter set forth.

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TransEnterix, Inc.

<April 28, 2017

Page 2

In delivering this opinion, 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 originals of all documents submitted to us as certified, photostatic or conformed copies, the authenticity of originals of all such latter documents, and the accuracy and completeness of all records, information and statements submitted to us by officers and representatives of the Company. In making our examination of documents executed by parties other than the Company, we have assumed that such parties had the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization of all requisite action, corporate or other, and execution and delivery by such parties of such documents and the validity and binding effect thereof with respect to such parties.

Based upon and subject to the limitations, qualifications and assumptions set forth herein, we are of the opinion that: (i) the Shares to be issued and sold by the Company have been duly authorized for issuance and, when issued and paid for in accordance with the terms and conditions of the Agreement, will be validly issued, fully paid and non-assessable; (ii) the Warrants to be issued and sold by the Company have been duly authorized for issuance and, when executed, issued and delivered by the Company in accordance with the terms and conditions of the Warrants, will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms; and (iii) the Warrant Shares issuable upon exercise of the Warrants have been duly authorized and reserved for issuance and, when issued and sold by the Company in accordance with the Warrants, will be validly issued, fully paid and non-assessable.

The opinions expressed herein are subject to the effect of applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, fraudulent transfer, marshalling or similar laws affecting creditors’ rights and remedies generally; general principles of equity, including without limitation, concepts of materiality, reasonableness, good faith and fair dealing (regardless of whether such enforceability is considered in a proceeding in equity or at law); and limitations on enforceability of rights to indemnification or contribution by federal or state securities laws or regulations or by public policy.

We express no opinion as to the laws of any jurisdiction other than the present federal laws of the United States of America and the present laws of the State of Delaware and the State of New York.

We hereby consent to the filing of this opinion with the Commission as an exhibit to a Current Report on Form 8-K (and its incorporation by reference into the Registration Statement) in accordance with the requirements of Item 601(b)(5) of Regulation S-K promulgated under the Securities Act, and to the use of this firm’s name therein and in the Prospectus Supplement under the caption “Legal Matters.” In giving such consent, we do not hereby 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.

Sincerely yours,

/s/ Ballard Spahr LLP