degree (1979) from the New England Conservatory of Music, where he studied jazz improvisation and composition with Ran Blake, George Russell, and Jaki Byard, and horn with Thomas Newell.

He has performed and recorded with Steve Lacy, Dave Liebman, George Gruntz, John Zorn, Bobby Watson, La Monte Young, Miles Davis with Quincy Jones, Bobby Previte, Jim McNeely, McCoy Tyner, Reggie Workman, the Mingus Orchestra, Franz Koglmann, and appears on more than 70 albums.

Varner's first two recordings as a leader were influenced by Ornette Coleman, Steve Lacy, Charles Mingus, Anthony Braxton, and minimalists such as Steve Reich and Philip Glass, and featured Varner's horn with alto sax (Ed Jackson), bass (Fred Hopkins or Ed Schuller) and drums (Billy Hart), with no chordal instrument.

His third recording was a more "straight-ahead" jazz project, with Kenny Barron, Jim Snidero, Mike Richmond, and Victor Lewis.

From that point (1987) on, most of Varner's work as a leader was for a quintet of horn and two saxes, bass, and drums, with frequent guest artists augmenting the ensembles.