Levey, who died Tuesday of cancer, taught himself to play drums and first played with Gillespie when he was 16, the Los Angeles Times reported Friday.
"He was everything a good drummer should be," jazz critic and historian Ira Gitler said Thursday. "His technique and his feel for the drums were used in the service of whatever group he was playing with, from Stan Kenton's large orchestra to piano trios."
He performed on more than 2,000 recordings with singers like Ella Fitzgerald and Peggy Lee and played on the sound tracks of more than 300 movies and some 3,000 TV show episodes.
Levey is survived by his wife of 53 years, three sons, seven grandchildren and five great-grandchildren.