A graduate of the Eastman School of Music, he studied under Arthur Berger, David Diamond, Aaron Copland and Nadia Boulanger.

[4] Strouse's next show was All American (1962), with a book by Mel Brooks and lyrics by Adams; it was not a success, closing after 80 performances,[5] but it produced the standard “Once Upon a Time” (recorded by Perry Como, Eddie Fisher, Al Martino, Tony Bennett, Frank Sinatra, and Bobby Darin, among dozens of others).

The musical It's a Bird, It's a Plane, It's Superman (1966, based on the popular comic strip) closed after 129 performances, but introduced the song "You've Got Possibilities" sung by Linda Lavin.

[8] In 1970, Applause (starring Lauren Bacall, with book by Betty Comden and Adolph Green, and lyrics by Adams) won Strouse his second Tony Award, for Best Musical.

[16] His film scores include Bonnie and Clyde (1967), There Was a Crooked Man... (1970, with Henry Fonda and Kirk Douglas), the Norman Lear production of The Night They Raided Minsky's (1968, with Adams) and the popular animated movie All Dogs Go to Heaven (1989).

His Concerto America, composed in 2002 to commemorate 9/11 and the spirit of New York City, premiered at The Boston Pops in 2002,[18] and his opera Nightingale (1982), starring Sarah Brightman, had a successful run in London, followed by many subsequent productions.

A musical stage adaptation of the Paddy Chayefsky film Marty starring John C. Reilly premiered at Boston's Huntington Theatre in October 2002, with lyrics by Lee Adams and Strouse and the book by Rupert Holmes.