Ernst & Young has named Carmine Di Sibio, the Big Four accounting firm’s global managing partner for client service, as its next global chairman and chief executive.

Mr. Di Sibio, a 33-year veteran of EY, was elected by the firm’s global board for a four-year term beginning July 1. He will succeed Mark Weinberger, who has led EY since 2013 and said in December that he would step down.

Mr....