Born in New York City, LaVerne studied at Juilliard School of Music, Berklee College, and the New England Conservatory, and took private lessons from jazz pianist Bill Evans.
LaVerne has worked with Frank Sinatra, Stan Getz, Woody Herman, Dizzy Gillespie, Chick Corea, Lionel Hampton, Michael Brecker and Elvin Jones.
A prolific recording artist, his projects as a leader number more than 50,[2] including Intuition, a duo with saxophonist Jerry Bergonzi (SteepleChase), and Epiphany (ClaveBop).
He is the author of Handbook of Chord Substitutions, Tons of Runs (Ekay), Bill Evans Compositions 19 Solo Piano Arrangements, and is the pianist on The Chick Corea Play-Along Collection (Hal Leonard).
He is the recipient of five Jazz Fellowships from the National Endowment for the Arts and winner of the 2000 John Lennon Songwriting Contest for his tune "Shania".