Exhibit 5.1

1735 Market Street, 51st Floor

Philadelphia, PA 19103-7599

TEL 215.665.8500

FAX 215.864.8999

www.ballardspahr.com

May 10, 2017

TransEnterix, Inc.

635 Davis Drive, Suite 300

Morrisville, NC 27713

RE: TransEnterix, Inc.

Ladies and Gentlemen:

We have acted as counsel to TransEnterix, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of the Company’s Registration Statement on Form S-3, dated the date hereof (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”), relating to the issuance and/or sale by the Company from time to time of an aggregate of up to $150,000,000 of (i) shares of common stock, par value $0.01 (the “Common Stock”), (ii) shares of preferred stock, par value $0.01 (“Preferred Stock”), (iii) senior and/or subordinated debt securities (the “Debt Securities”), (iv) warrants (the “Warrants”) and (v) units composed of any of the foregoing (the “Units”). The Common Stock, the Preferred Stock, the Debt Securities, the Warrants and the Units are collectively referred to in this opinion as the “Securities.”

The Company has informed us that the Securities will be sold or delivered on a delayed or continuous basis from time to time as set forth in the Registration Statement (and any amendments thereto), the prospectus contained therein and any prospectus supplement. We understand that prior to the sale of any Securities under the Registration Statement, the Company will afford us an opportunity to review the operative documents pursuant to which such Securities are to be sold and will file any applicable amendment to the Registration Statement or Current Report on Form 8-K (which may include as an exhibit an amendment to this opinion) or prospectus supplement as we may reasonably consider necessary or appropriate by reason of the terms of the sale of such Securities.

In so acting, we have examined originals or copies (certified or otherwise identified to our satisfaction) of (i) the Amended and Restated Certificate of Incorporation of the Company, together with all amendments thereto; (ii) the Amended and Restated Bylaws of the Company; (iii) the Registration Statement and the exhibits thereto; (iv) the prospectus contained within the Registration Statement; (v) such corporate records, agreements, documents and other instruments; and (vi) such certificates or comparable documents of public officials and other sources believed by us to be reliable, and of officers and representatives of the Company, and have made such inquiries of such officers and representatives, as we have deemed relevant and necessary as a basis for the opinions hereinafter set forth.

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In such examination, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed or photostatic copies and the authenticity of the originals of such latter documents. As to all questions of fact material to this opinion that have not been independently established, we have relied upon certificates or comparable documents of officers and representatives of the Company.

We have also assumed that (i) the Registration Statement and any amendments or supplements thereto (including any post-effective amendments) will have become effective and comply with all applicable laws and no stop order suspending the Registration Statement’s effectiveness will have been issued and remain in effect, in each case, at the time the Securities are offered or issued as contemplated by the Registration Statement, (ii) a prospectus supplement will have been prepared and filed with the Commission describing the Securities offered thereby and will at all relevant times comply with all applicable laws, (iii) the Company has timely filed all necessary reports pursuant to the Securities Exchange Act of 1934, as amended, which are incorporated into the Registration Statement by reference, (iv) all Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the appropriate prospectus supplement, (v) a definitive purchase, underwriting or similar agreement and any other necessary agreement with respect to any Securities will have been duly authorized and validly executed and delivered by the Company and the other party or parties thereto and (vi) any Securities issuable upon conversion, exercise or exchange of any Securities being offered or issued will be duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exercise or exchange.

Based on the foregoing, and subject to the qualifications stated herein, we are of the opinion that:

1. Common Stock. Assuming that the issuance and terms of any Common Stock and the terms of the offering thereof have been duly authorized, when (i) the Company has received the consideration therefore specified in any applicable underwriting agreement or purchase agreement approved by the Company’s board of directors or any authorized committee thereof, (ii) the consideration for such Common Stock is at least equal to the aggregate par value of such Common Stock, (iii) in the case of any Common Stock to be issued under any Warrants, upon due exercise and delivery of any payment of the exercise price specified in such Warrants, and (iv) in the case of any Common Stock to be issued upon the exchange or conversion of Debt Securities, Preferred Stock, Warrants and other rights that are exchangeable for or convertible into Common Stock, due exercise of such exchange or conversion rights in accordance with the terms of the applicable instruments, such Common Stock (including any Common Stock that may be issued as part of Units or upon exercise, conversion, exchange or otherwise pursuant to the terms of any other Securities) will be validly issued, fully paid and non-assessable.

2. Preferred Stock. Assuming that the issuance and terms of any series of Preferred Stock and the terms of the offering thereof have been duly authorized, when (i) a Certificate of Designation fixing and determining the terms of the Preferred Stock has been duly filed with the Secretary of State of the State of Delaware and accepted for record, (ii) the Company has received the consideration therefore specified in any applicable underwriting agreement or purchase agreement approved by the Company’s board of directors or any authorized committee thereof, (iii) the consideration for such Preferred Stock is at least equal to the aggregate par value of such Preferred Stock and (iv) in the case of any Preferred Stock to be issued under any Warrants, upon due

exercise and delivery of any payment of the exercise price specified in such Warrants, such Preferred Stock (including any Preferred Stock that may be issued as part of Units or upon exercise, conversion, exchange or otherwise pursuant to the terms of any other Securities) will be validly issued, fully paid and non-assessable.

3. Debt Securities. Assuming that the issuance and terms of any Debt Securities and the terms of the offering thereof have been duly authorized, when (i) an indenture filed as an exhibit to the Registration Statement (an “Indenture”) has been duly executed, authorized and delivered by all parties thereto substantially in the form so filed, and any applicable supplemental indenture relating to such Debt Securities has been duly executed, authorized and delivered by all parties thereto, (ii) the terms of the Debt Securities to be issued under the applicable Indenture and any applicable supplemental indenture and of their issuance and sale have been duly established in conformity with such Indenture and any applicable supplemental indenture so as not to violate any applicable law, affect the enforceability of such Debt Securities or result in a default under or breach of any agreement or instrument binding on the Company, and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, and (iii) the Debt Securities have been duly executed and authenticated in accordance with such applicable Indenture and any applicable supplemental indenture and issued and sold as contemplated in the Registration Statement and any prospectus supplement relating thereto, and in accordance with any underwriting agreement or purchase agreement approved by the Company’s board of directors or any authorized committee thereof, such Debt Securities (including any Debt Securities that may be issued as part of Units or otherwise pursuant to the terms of any other Securities) will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

4. Warrants. Assuming that the issuance and terms of such Warrants and the terms of the offering thereof have been duly authorized, when (i) the Warrant agreement or Warrant agreements relating to such Warrants have been duly authorized, executed and delivered by the Company and the warrant agent has been appointed by the Company, (ii) the terms of such Warrants have been duly established so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental or regulatory body having jurisdiction over the Company, and (iii) such Warrants and any certificates representing such Warrants have been duly executed, authenticated, issued, paid for and delivered as contemplated in the Registration Statement and any prospectus supplement relating thereto, and in accordance with any underwriting agreement or purchase agreement approved by the Company’s board of directors or any authorized committee thereof, such Warrants (including any Warrants that may be issued as part of Units or otherwise pursuant to the terms of any other Securities) will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

5. Units. Assuming that the issuance and terms of such Units and the terms of the offering thereof have been duly authorized, when (i) the Unit agreement or Unit agreements relating to such Units have been duly authorized, executed and delivered by the Company and the warrant agent appointed by the Company, (ii) the terms of such Units have been duly established so as not to violate any applicable law, affect the enforceability of such Units or result in a default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental or regulatory body having jurisdiction over the Company, and (iii) such Units have been duly executed and authenticated in

accordance with the applicable Unit agreement and issued, paid for and delivered as contemplated in the Registration Statement and any prospectus supplement relating thereto, and any underwriting agreement or purchase agreement approved by the Company’s board of directors or any authorized committee thereof, such Units (including any Units that may be issued upon exercise, conversion, exchange or otherwise pursuant to the terms of any other Securities) will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

The opinions expressed above with respect to validity, binding effect and enforceability are subject to applicable bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and similar laws affecting creditors’ rights and remedies generally, and subject, as to enforceability, to general principles of equity, including principles of commercial reasonableness, good faith and fair dealing (regardless of whether enforcement is sought in a proceeding at law or in equity) and except that rights to indemnification and contribution thereunder may be limited by federal or state securities laws or public policy relating thereto.

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

We hereby consent to the use of this letter as an exhibit to the Registration Statement and to any and all references to our firm in the prospectus which is a part of the Registration Statement.

Sincerely yours,

/s/ Ballard Spahr LLP