Tompkins attended the New England Conservatory of Music, then moved to New York City, where he worked with Kai Winding (1960–67), Eric Dolphy (1964), Wes Montgomery (1966), Bob Brookmeyer/Clark Terry (1966), Benny Goodman (1968), Bobby Hackett (1965–70), and Al Cohn and Zoot Sims (1968–72). He moved to Los Angeles in 1971, playing with Louie Bellson, Joe Venuti, and Red Norvo in the 1970s and Jack Sheldon in the 1980s. He was perhaps best known for his longtime association with Doc Severinsen's The Tonight Show Band, in which he played from the 1970s until 1992. He recorded prolifically for Concord Jazz as a leader in the second half of the 1970s.
Tompkins died of lung cancer in 2006.
- A Pair to Draw To (Concord Jazz, 1975)
- Scrimshaw (Concord, 1976)
- Live at Concord 1977 (Concord, 1977)
- Lost in the Stars (Concord, 1977)
- Ross Tompkins and Good Friends (Concord, 1978)
- Festival Time (Concord, 1979)
- Street of Dreams (Famous Door, 1982)
- Solo Piano (Progressive Records, 1994)
- Celebrates the Music of Jule Styne (Progressive, 1996)
- Heart To Heart (HD Records, 1998) Ross Tompkins and Cathy Segal-Garcia
- Ross Tompkins Celebrates the Music of Harold Arlen (Progressive, 1999)
- Younger than Springtime (Arbors Records, 2001)
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- Lock, the Fox (RCA Victor, 1966)
With Kai Winding
- The Incredible Kai Winding Trombones (Impulse!, 1960)
- Israel (A&M/CTI, 1968) with J. J. Johnson
- Stonebone (A&M/CTI (Japan), 1969) with J. J. Johnson
With Snooky Young
- Paul Rinzler, "Ross Tompkins". The New Grove Dictionary of Jazz.
- Richard S. Ginell, Ross Tompkins at Allmusic
- Obituary, New York Times, July 9, 2006.