Following a short stint studying mathematics at the City College of New York, he enrolled at the Juilliard School of Music, where he received a Bachelor of Science degree in 1942.

[4] Following the war, Henderson began a long professional association with a number of musical notables of the era, including Duke Ellington, Lena Horne, Jule Styne, and Richard Rodgers.

"[4][6] Henderson's first foray into Broadway theatre was Ellington's Beggar's Holiday, serving as co-orchestrator alongside Billy Strayhorn.

[8] Henderson additionally made his Broadway songwriting debut with Jelly's Last Jam, receiving a 1992 Tony Award nomination for Best Original Score, alongside lyricist Susan Birkenhead.

[4] From the 1950s on, Henderson also worked extensively in television, including The Ed Sullivan Show, The Bell Telephone Hour, and specials for Dean Martin, Carol Burnett, Andy Williams, and Victor Borge.

[2] Henderson served as musical director for actress Polly Bergen and Victor Borge; and arranged music for many popular singers, including Robert Goulet, Nancy Wilson, Ben Vereen, Sandler and Young, Leslie Uggams, Eartha Kitt, Diahann Carroll, Dinah Shore, Eileen Farrell, Juliet Prowse, and Liza Minnelli.