The 37-year-old Stein will take over in April from Philip Gourevitch, who announced last fall he would step down after five years. Stein is currently an editor at Farrar, Straus & Giroux.
The Paris Review was founded in 1953 and was run for decades by George Plimpton, who died in 2003. The magazine announced Stein's appointment Friday.
It has published early work by Jack Kerouac and Philip Roth, among others. It is famous for its literary interviews.