Born in Newport, Rhode Island, Anderson was a street magician before becoming an actor. He is famous for the role of Judge Harold T. Stone on the 1983-1992 television series Night Court. In addition to eight appearances on Saturday Night Live between 1981 and 1985, Anderson had a recurring guest role as con man "Harry the Hat" on Cheers, toured extensively as a magician, and did several magic/comedy shows for broadcast, including Harry Anderson's Sideshow (1987).

In the 1990s Anderson starred in the sitcom Dave's World, based loosely on the life and columns of humor columnist Dave Barry. Together with long-time friend Turk Pipkin, Anderson wrote a book called Games You Can't Lose - A Guide For Suckers, a collection of gags, cons, tricks and scams. First published in 1989 (ISBN 1580800866—2001 reprint), this title also contains a survey of "Games You Can't Win" told from an insider's perspective.

A long-time Mel Tormé fan, Anderson and his wife Elizabeth currently (2005) own a small shop in the French Quarter of New Orleans named "Sideshow" selling various "magic, curiosities, and apocrypha." In the summer of 2005, Anderson also opened a nightclub in the French Quarter called Oswald's Speakeasy, located at 1331 Decatur Street, New Orleans.