Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in Registration Statements No. 333-193098 and No. 333-180219 on Form S-8 and Registration Statement No. 333-188728 and No. 333-201827 on Form S-3 of our reports dated November 24, 2015, relating to the consolidated financial statements of M/A-COM Technology Solutions Holdings, Inc., and the effectiveness of M/A-COM Technology Solutions Holdings, Inc.’s internal control over financial reporting (which report expresses an adverse opinion on the effectiveness of the Company’s internal control over financial reporting because of a material weakness) appearing in this Annual Report on Form 10-K for the year ended October 2, 2015.

/s/ Deloitte & Touche LLP

Boston, Massachusetts

November 24, 2015