Exhibit 5.1

|  | ORRICK, HERRINGTON & SUTCLIFFE LLP 1000 Marsh Road Menlo Park, CA 94025-1015 United States tel +1 650-614-7400 fax +1 650-614-7401 WWW.ORRICK.COM

October 17, 2018

Twist Bioscience Corporation

455 Mission Bay Boulevard

Suite 545

San Francisco, CA 94158

Re: | Registration Statement on Form S-1

Ladies and Gentlemen:

We are acting as counsel for Twist Bioscience Corporation, a Delaware corporation (the “Company”), in connection with the registration statement on Form S-1 filed by the Company with the Securities and Exchange Commission (the “Commission”) on October 3, 2018 (File No. 333-227672), as amended (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”). The Registration Statement relates to the registration of 5,000,000 shares of common stock of the Company, par value $0.00001 per share, (the “Primary Shares”) and 750,000 shares of which may be purchased by the underwriters pursuant to an option to purchase additional shares (together with the Primary Shares, the “Shares”). We understand that the Shares are to be sold to the underwriters for resale to the public as described in the Registration Statement and pursuant to an underwriting agreement, substantially in the form filed as an exhibit to the Registration Statement, to be entered into by and among the Company and the underwriters (the “Underwriting Agreement”).

In connection with rendering the opinion set forth below, we have examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of instruments, documents, and records which we deemed relevant and necessary for the purpose of rendering our opinion set forth below. In such examination, we have assumed the following: (a) the authenticity of original documents and the genuineness of all signatures, (b) the conformity to the originals of all documents submitted to us as copies, (c) the representations of officers and employees are correct as to questions of fact, (d) the Registration Statement has been declared effective pursuant to the Securities Act and (e) a pricing committee of the board of directors will have taken action necessary to set the sale price of the Shares.

Our opinion herein is limited to the General Corporation Law of the State of Delaware.

Based upon the foregoing, we are of the opinion that the Shares to be issued and sold by the Company have been duly authorized and, when such Shares are issued and paid for in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid and non-assessable.

Twist Bioscience Corporation

Registration Statement on Form S-1

October 17, 2018

Page 2

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Legal matters” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission promulgated thereunder, nor do we thereby admit that we are “experts” within the meaning of such term as used in the Securities Act with respect to any part of the Registration Statement, including this opinion letter as an exhibit or otherwise.

Very truly yours,

/s/ Orrick, Herrington & Sutcliffe LLP

ORRICK, HERRINGTON & SUTCLIFFE LLP