Keller was born in Chicago and attended University of Illinois, where he began writing comedy with his fraternity brother Allan Sherman.
His notable screenplays include Buona Sera, Mrs. Campbell (written with Melvin Frank and Denis Norden), which would later become the inspiration for the stage and film musical Mamma Mia!
In the early 1980s, as his writing career was winding down, Keller formed the Beverly Hills Unlisted Jazz Band with friends Conrad Janis and George Segal.
Their mix of jazz and comedy made them popular enough to play at Carnegie Hall and on The Tonight Show and led to their own PBS special in 1993, "This Joint Is Jumpin'".
In later life, Keller collaborated with his friend Howard Albrecht on Funny Stuff, a newsletter of jokes for radio DJs and public speakers.