Born in Kotor, a small Montenegrin coastal town in the former Yugoslavia, the pianist was classically trained as a child but was also drawn to the jazz he heard on Armed Forces Radio and Voice of America during World War II and the Communist regime that followed.

The young pianist began listening to KJAZ radio, hanging out at record shops, and frequenting clubs to hear Miles Davis, John Coltrane, Dizzy Gillespie, and Bill Evans.

Guaraldi featured Vuckovich in a two-piano quintet, Powder Keg, and sent him to substitute as accompanist for vocalists Irene Kral and David Allyn.

Vuckovich worked with Philly Joe Jones in San Francisco at the Keystone Korner, where he was a resident pianist for five years.

Vuckovich worked for five years in New York City, where he performed at the Village Vanguard, Blue Note Jazz Club, Bradley's Zinno, West End, and Hanratty's, working with Al Cohn, Curtis Fuller, Tom Harrell, Billy Higgins, Milt Hinton, Mel Lewis, Red Mitchell, Michael Moore, and Cecil Payne.

He led bands that included Walter Booker, Joshua Breakstone, Dennis Irwin, Victor Lewis, and Harvie S. He returned to San Francisco for a long-term engagement from 1990 to 1997 as house pianist and music director of Club 36 at the Grand Hyatt Hotel.

He performed in New York at Lincoln Center's Dizzy's Club Coca Cola and was Marian McPartland's guest on her NPR program Piano Jazz.