William Selditz, a close family friend, told the Los Angeles Times Shaughnessy suffered a fatal heart attack Friday at his home in Calabasas, Calif.
In addition to playing on TV's "The Tonight Show" from 1963 to 1992, the New Jersey native also performed with music icons such as Billie Holliday, Aretha Franklin, Jimi Hendrix, John McLaughlin, Leonard Bernstein and the New York Philharmonic, George Balanchine and the New York City Ballet, and the Benny Goodman, Count Basie and Tommy Dorsey bands, the Times said.
Severinsen described him in Shaughnessy's 2010 memoir "Lucky Drummer" as "the superb engine that drove our Tonight Show Band for 30 years ... with spirit and immense skill."
Shaughnessy was married to singer Ilene Woods -- the voice of Disney's Cinderella -- from 1963 until her death in 2010.
He is survived by his son, Daniel, his daughter-in-law, Nicah, and three grandchildren. Another son, Jimmy, died in a 1984 traffic accident, the Times said.