The Bronx-born Harnell, who studied music at the University of Miami, toured with the Glenn Miller Air Force band during World War II.
During the war, he studied composition with Nadia Boulanger in Paris and William Walton at the Trinity College of Music in London. After the war, he studied with Aaron Copland at Tanglewood.
He worked with the singer Peggy Lee in the 1950s and '60s, conducting the orchestra for two of her albums and playing piano on Things Are Swingin'.
Harnell also worked in various capacities—pianist, arranger, music director—with such singers as Lena Horne, Frank Sinatra, Shirley MacLaine, Marlene Dietrich, Pearl Bailey, Judy Garland, and Beverly Sills.
With his own orchestra, he recorded Fly Me to the Moon Bossa Nova.
In the late '60s and early '70s, he worked as music director for Mike Douglas' television show, and scored a number of television shows and films.