Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in Registration Statements on Form S-3 (Nos. 333-119796, 333-117346 and 333-111121) and on Form S-8 No. 333-128206 of our reports dated March 15, 2006, relating to the consolidated financial statements of iBasis, Inc. and subsidiaries, and management’s report on the effectiveness of internal control over financial reporting, appearing in this Annual Report on Form 10-K of iBasis, Inc. and subsidiaries for the year ended December 31, 2005.

/s/ DELOITTE & TOUCHE LLP

Boston, Massachusetts

March 15, 2006