Fleck was born in New York City, New York, and is named after famous Hungarian composer Béla Bartók, Austrian composer Anton Webern, and Czech composer Leoš Janáček. He was drawn to the banjo when he first heard Earl Scruggs play the theme song for the television show Beverly Hillbillies. He received his first banjo at age fifteen from his grandfather (1973). Later, Fleck enrolled in New York City's High School of Music and Art where he studied the French horn. He was a banjo student under Tony Trischka.

Almost immediately after high school, Fleck traveled to Boston to play with Jack Tottle, Pat Enright, and Mark Schatz in Tasty Licks. During this period, Fleck released his first solo album (1979): Crossing the Tracks and made his first foray into progressive bluegrass composition.

Fleck played on the streets of Boston with bassist Mark Schatz; and the two, along with guitarist/vocalist Glen Lawson and mandolin great Jimmy Gaudreau, formed Spectrum: the Band in 1981. Fleck toured with Spectrum during 1981. That same year, Sam Bush asked Fleck to join New Grass Revival. Fleck performed with New Grass Revival for nine years. During this time, Fleck recorded another solo album, Drive. It was nominated for a Grammy Award in the then first-time category of "Best Bluegrass Album" (1988).

During the 1980s Fleck and Bush also performed live occasionally with Doc Watson and Merle Watson in various bluegrass festivals, most notably the annual Telluride Bluegrass Festival.

Béla Fleck and Victor Wooten formed Béla Fleck and the Flecktones in 1988, along with keyboardist and harmonica player Howard Levy and Wooten's percussionist brother Roy "Future Man" Wooten, who played synthesizer-based percussion. Levy left the group in 1992, making the band a trio until Saxophonist Jeff Coffin joined the group onstage part-time in 1997, eventually becoming a permanent member. His first studio recording with the band was their 1998 album Left of Cool. In 1996, he appeared on the tribute album to Hank Marvin, one of his influences, and The Shadows "Twang" playing a Shadows UK hit from the 1960s, "The Stranger".

With the Flecktones, Fleck has been nominated for and won several Grammy awards. (Cf. Grammy sections below.)

Fleck has shared Grammy wins with Asleep at the Wheel, Alison Brown, and Edgar Meyer. He has been nominated in more categories than any other musician, namely country, pop, jazz, bluegrass, classical, folk, spoken word, composition, and arranging.

In 2001, Fleck collaborated with long-time friend and playing-partner Edgar Meyer to record Perpetual Motion, an album of classical material played on the banjo along with an assortment of accompanists, including John Williams, Evelyn Glennie, Joshua Bell and Gary Hoffman. The album includes selections such as Chopin's Etude Op. 10 No. 4 in C# minor, Debussy's Doctor Gradus ad Parnassum, and Paganini's Moto Perpetuo (from which is derived the name), as well as more lyrical pieces such as the first movement of Beethoven's Moonlight Sonata, two of Chopin's mazurkas, and two Scarlatti keyboard sonatas. Perpetual Motion won two Grammys at the Grammy Awards of 2002 for Best Classical Crossover Album and Best Arrangement for Fleck and Meyer's arrangement of Doctor Gradus ad Parnassum. Fleck and Meyer have also composed a double concerto for banjo and bass, and performed its debut with the Nashville Symphony Orchestra.

Fleck names Chick Corea, Charlie Parker, and the aforementioned Earl Scruggs as influences. He regards Scruggs as "certainly the best" banjo player of the three-finger style.

Solo and with the Flecktones, Fleck has appeared at Telluride Bluegrass Festival, Merlefest, Montreal International Jazz Festival, Toronto Jazz Festival, Newport Folk Festival, Austin City Limits Music Festival, Bonnaroo, and Jazzfest, among others.