After a few minor roles in films for Warner Bros., Anderson got his big break in the 1941 picture Navy Blues, starring Martha Raye and Ann Sheridan, followed by The Body Disappears and The Male Animal in which he co-starred with Henry Fonda and Olivia de Havilland. His other films include the 1949 World War II film Battleground, Give My Regards to Broadway, Excuse My Dust, Island in the Sky, The Benny Goodman Story, Kelly and Me, Joe Butterfly, My Man Godfrey (1957), I Bury the Living, Sunrise at Campobello, Hold On! and Rascal. Anderson also acted extensively in Broadway shows, including the role of Dr. Bird in The Caine Mutiny Court-Martial. He was also in the film version of The Caine Mutiny, with Humphrey Bogart; he was the only actor to appear in both the Broadway play and film.