He began as a writer for Danny Thomas radio show during 1940s, and wrote for Martin and Lewis and Bob Hope. On 1950s television he worked for Sid Caesar, along with other gifted comedy writers Woody Allen, Neil Simon, Mel Brooks and Carl Reiner.
He wrote the long-running Broadway farce A Funny Thing Happened on the Way to the Forum with Burt Shevelove and Stephen Sondheim in 1962, and collaborated with Shevelove on a series of UK movie comedies during rest of 1960s.
In 1972 he returned to the United States to produce and write many episodes of the TV version of the novel/movie M*A*S*H*.
He also wrote the screenplays to Oh, God and Movie Movie, and in 1982 co-wrote the Oscar-nominated screenplay for Tootsie.
Broadway credits include libretto for musical City of Angels and Iran-contra satire Mastergate; in the early 1960s, uttered the now-classic line, "If Hitler is alive, I hope he's out of town with a musical." TV credits include cable TV-movie Barbarians at the Gate. Wrote memoirs, Laughing Matters, in 1997.
Gelbart is sometimes known as Francis Burns in the credits.