<Page> EXHIBIT 23.1 INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in Registration Statement Nos. 333-30642, 333-56998, 333-67780, and 333-73492 on Form S-8 and Registration Statement No. 333-53756 on Form S-3 of iBasis, Inc. of our report dated March 7, 2003 related to the consolidated financial statements of iBasis, Inc. as of and for the two years ended December 31, 2002 (which report expresses an unqualified opinion and includes an explanatory paragraph relating to a change in the method of accounting for goodwill and other intangible assets), appearing in the Annual Report on Form 10-K of iBasis, Inc. for the year ended December 31, 2002. /s/ Deloitte & Touche LLP Boston, Massachusetts March 25, 2003