Reich was born in New York City. He attended City and Country School and Lincoln School in the city prior to undergraduate studies at Oberlin College. As a law student, he was editor-in-chief of the Yale Law Journal for 1951–1952 and he clerked for U.S. Supreme Court Justice Hugo L. Black during the 1953-1954 term. Prior to his academic career he worked for six years as a lawyer at the leading firms Cravath, Swaine & Moore in New York and Arnold & Porter in Washington, D.C..
Reich was a professor at Yale Law School from 1960-1974. Both Bill Clinton and Hillary Rodham Clinton were students of Professor Reich when he was writing The Greening of America and he is mentioned in their biographies. Reich left Yale in 1974 to move to San Francisco, although he continued as a visiting professor from 1974-1976. He returned to teach at Yale from 1991–1994 and in February 2011. The Yale Law School Association selected Reich for its Award of Merit in 2008.