Wolsky was born in Paris, France, but during World War II, he and the rest of his family fled to the United States to escape the German occupation.

[1] He began his career as costume designer for the theatre by assisting costume designer Ann Roth on A Case of Libel (1963);[2] he later assisted Roth on The Odd Couple (1965), Patricia Zipprodt on Fiddler on the Roof (1964), and Theoni Aldredge on Illya Darling (1967).

[5] He went on to serve as principal costume designer for both plays and musicals, including The Sunshine Boys (1972) and Sly Fox (1976).

He won his second Academy Award for Bugsy in 1991 and has been nominated five other times, most recently for his work on Julie Taymor's Beatles-inspired musical Across the Universe (2007) and Sam Mendes's Revolutionary Road (2008).

In 2010, Wolsky donated his costume design sketches to the Margaret Herrick Library at the Academy of Motion Picture Arts and Sciences.