Weisfeiler, a Jew, was born in the Soviet Union. He received his Ph.D. in 1970 from the Steklov Institute of Mathematics Leningrad Department, as a student of Ernest Vinberg. In the early 1970s, Weisfeiler was asked to sign a letter against a colleague, and for his refusal was branded "anti-Soviet". Weisfeiler left the Soviet Union in 1975 to be free to advance his career and practice his religion. After a brief period under Armand Borel at the Institute for Advanced Study, near Princeton University, Weisfeiler became a professor at Pennsylvania State University. In 1981, he was naturalized as an American citizen.