The 68-year-old Tompkins died on June 30 at his St. Augustine home from lung cancer, The New York Times said.
A graduate of the New England Conservatory of Music, Tompkins first joined the orchestra on the "Tonight" show in 1971 and remained with the ensemble until Johnny Carson left the show as its host.
During his musical career, Tompkins played alongside jazz greats such as singer Jack Sheldon, drummer Louie Bellson, and clarinetist Benny Goodman.
The Times said Tompkins is survived by three daughters, Janine, Suzie and Teri; five grandchildren and his brother, Rick.
Celebrity Families of 2014 [PHOTOS]