Regev was born in Poland and emigrated to Israel in 1958. His academic career was mainly in Israel. He studied physics and mathematics at the Hebrew University of Jerusalem, with graduate studies and a Ph.D. at Tel Aviv University, and became a faculty member at the Technion – Israel Institute of Technology. During his studies he served four years in the Israel Defense Forces and continued to serve in the reserve units, reaching the rank of major. In 2002 he moved to the US.