A graduate of Northwestern University, Furth began his career as a performer, appearing on Broadway in A Cook for Mr. General and Hot Spot, and appeared in numerous films and television shows for over 35 years, including Butch Cassidy and the Sundance Kid, Blazing Saddles, and Murder, She Wrote.
Furth originally wrote Company as a series of one-act plays. He later collaborated with Sondheim on Merrily We Roll Along, which was adapted from a play by George S. Kaufmann and Moss Hart, and the thriller Getting Away With Murder.
In addition, he wrote the book for the John Kander-Fred Ebb musical The Act, and authored the plays Twigs, Precious Sons, and The Supporting Cast. He also wrote the teleplay for the 1975 version of Twigs, which starred Carol Burnett, Edward Asner, and Jack Gilford.