Enzo Randisi was born in Palermo on January 16, 1935, to a bank-official father and a schoolteacher mother. He was largely self-taught. Palermo's Balarm news site reports that he came to jazz through the American soldiers stationed in the city after the Second World War, and that V-disc recordings by Lionel Hampton pointed him toward the vibraphone. Palermo's municipal biographical archive says he began on trombone, moved to piano and other instruments, and settled on the vibraphone. In the 1950s he played at Palermo's Hotel Sole with pianist Livio Civiletti and bassist Luigi Pernice, and he later gave up a steady job to play jazz full time.

In 1963 he was billed as a star of world renown at the Jazz Festival in Comblain-la-Tour, Belgium. RAI critic and programmer Adriano Mazzoletti called him one of the world's most important vibraphonists, and he played concerts from the United States to Turkey, Spain and the former Soviet Union. The municipal archive lists him as a co-founder of the Brass Group, the Palermo jazz organization that later became a foundation, and as a talent scout for young Sicilian jazz musicians. He also arranged for a vocal group, the Duke Ellington Singers, and appeared with the Montecarlo Night orchestra.

On January 16, 1976, his 41st birthday, he played piano in Chet Baker's quartet at the Brass Club in Palermo, alongside bassist Giovanni Tommaso and drummer Gianni Cavallaro. The recording was issued in 2011 as I Can't Get Started: Live in Palermo 1976 and in 2022 on vinyl as Blue 'N' Boogie. Musica Jazz's review of the CD describes him as a great vibraphonist who played piano on this date.

His own records begin with a four-track private-press LP, Enzo Randisi (P.D.R., 1979). It has his son Riccardo on Rhodes piano and ARP synthesizer, Giuseppe Costa on electric bass, Enzo Palacardo on electric guitar, Franco Lotà on drums and Mimmo Cafiero on percussion, and Discogs tags it Modal and Jazz-Funk. Percussionist Mimmo Cafiero was a member of Randisi's group from 1978 to 1981 and, per Italian Wikipedia, joined him on a twenty-concert tour of Spain. In 1981 Randisi led the Swing Ensemble on an LP for his own Ransemble label, recorded at ZIZ Studio 5 in March, a swing and modal program with the sisters Cinzia and Loredana Spata on vocals. A 1991 quartet album, Ten Years After (Splasc(h)), is a standards program with pianist Salvatore Bonafede, bassist Giuseppe Costa and Cafiero. In 2003 Philology released Mister Vibes Plays Milt, a tribute to Milt Jackson with pianist Giovanni Mazzarino, bassist Luciano Milanese and drummer Bobby Durham. A Palermo city cultural listing says John Lewis, leader of the Modern Jazz Quartet, invited Randisi to the Bled jazz festival and that the friendship lasted until Lewis's death in 2001.

He worked as a sideman too. Discogs credits him on vibraphone on Romano Mussolini's R.M. Record LP Swing Swing Swing, on Lino Patruno & The Jazz Stars of Italy's Live in San Marino (Carosello; the same session has Mussolini on piano, Carlo Loffredo on bass and Gil Cuppini on drums), on the 1987 LP Italian Clarinet Summit with clarinetists Bruno Longhi and Gianni Sanjust, and on the 1982 We Remember You by the Modern Art Quartet. Balarm's obituary also names 18 collaborators, among them Enrico Pieranunzi, Franco D'Andrea, Enrico Intra, Dado Moroni, Stephane Grappelli, Diane Schuur, Gianni Basso, Gil Cuppini, Bob Wilber, Al Grey, Bill Russo, Salvatore Bonafede and Bobby Durham; those credits come from the obituary and are not itemized on Discogs.

Randisi died at Palermo's Cervello Hospital on February 27, 2006. His last concert, by Balarm's account, was on Epiphany, January 6, at Teatro Politeama in Palermo, where he played "A Night in Tunisia." His sons Riccardo (piano) and Beppe (saxophone) are also musicians. The Eating Standing label brought the 1979 LP back into print in November 2023 and the Swing Ensemble LP in July 2024, and a first Enzo Randisi Memorial was held at the Spasimo in Palermo on January 16, 2023. On April 11, 2024, Riccardo organized a tribute at Palermo's Real Teatro Santa Cecilia where Padua vibraphonist Giovanni Perin played Randisi's restored Musser vibraphone.

The record shows a player formed by Lionel Hampton's swing-era vibraphone and, later, by Milt Jackson and the John Lewis-led Modern Jazz Quartet, whose repertoire fills Mister Vibes Plays Milt and whose pieces "Django" and "Milano" he recorded. His own bands ran across styles. The 1979 LP moves from the modal opener "Windows," a Chick Corea composition, to the electric funk of "Probu Zeni," a cover of a Karel Ruzicka piece, while the 1981 Swing Ensemble LP mixes Horace Silver, Ellington and Miles Davis titles with vocal arrangements. He also wrote library music, with composer credits on four tracks of the RAI production-music LP New Sound And Percussion (1987).