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 (i) our report dated June 11, 2007 relating to the consolidated financial statements of iBasis, Inc. and subsidiaries (which report expressed an unqualified opinion and includes explanatory paragraphs relating to (a) the Company’s adoption of Statement of Financial Accounting Standards No. 123(R), “Share Based Payment” and (b) the Company’s restatement of its 2005 and 2004 financial statements) and (ii) our report dated June 11, 2007 relating to 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, 2006.

/s/ DELOITTE & TOUCHE LLP

Boston, Massachusetts

June 11, 2007