Tony Scott was born Anthony Joseph Sciacca on June 17, 1921, in Morristown, New Jersey, the son of Sicilian immigrants. He started on a metal clarinet at 12, formed his first band at 14, quickly mastered the piano, and was sitting in at Harlem jam sessions by 18. He attended the Juilliard School from 1940 to 1942, auditioning on piano with Duke Ellington's "Sophisticated Lady," and played in Army bands during the Second World War. In 1943 he first heard Charlie Parker and resolved to bring Parker's bebop language to the clarinet; the two often played together, and Scott later called Parker the greatest man, not only the greatest musician, of the century.

His earliest records date from 1946, when he arranged and played clarinet on Gotham sides by a septet that included Ben Webster and trombonist Trummy Young, with Sarah Vaughan singing "All Too Soon." He appears, uncredited on clarinet and alto saxophone, on a Claude Thornhill orchestra session for RCA Victor on April 27, 1949, and he is credited on clarinet on Vaughan's 1950 Columbia sessions with George Treadwell's All Stars, a group that included Miles Davis on at least one track. According to his Los Angeles Times obituary, he also sat in the saxophone sections of the bands of Ellington, Tommy Dorsey and Buddy Rich. In 1953 he cut quartet sides for Brunswick with pianist Dick Katz, bassist Milt Hinton and drummer Philly Joe Jones, and that year the critic Nat Hentoff wrote in DownBeat that no other modern clarinetist matched his fire, drive and beat. DownBeat's critics named him the top clarinetist in 1955, 1957, 1958 and 1959.

His main base in the mid-1950s was RCA Victor. Scott's Fling (a septet recorded between December 1954 and January 1955, with trumpeter Jimmy Nottingham, trombonist Billy Byers, Danny Bank on baritone saxophone and Ed Wasserman on tenor), The Touch of Tony Scott and Both Sides of Tony Scott (both 1956) and the big-band The Complete Tony Scott (1957) made his case as a modern clarinetist with arranging ideas of his own. In those years he was also music director for Harry Belafonte and wrote the arrangement of "Banana Boat Song (Day-O)"; Discogs credits "Tony Scott and His Orchestra and Chorus" on Belafonte's 1956 album Calypso. For Billie Holiday he led the orchestra on studio dates on February 14, 1955, and June 7, 1956, played clarinet on her Clef album Lady Sings the Blues, and was credited on clarinet at her Carnegie Hall concert of November 10, 1956. A young Bill Evans and Paul Motian were his sidemen on several recordings made between 1957 and 1959, among them a session in New York on November 16, 1957, that also had trombonist Jimmy Knepper, trumpeter Clark Terry and baritone saxophonist Sahib Shihab, and was issued as The Modern Art of Jazz and Free Blown Jazz. Club dates at the Showplace in August 1959 with Evans, bassist Jimmy Garrison and drummer Pete La Roca, and a studio session on October 28 and 29, 1959, with Evans, bassist Scott LaFaro and Motian, were released decades later as Golden Moments and Sung Heroes.

In 1957 he toured Europe and visited South Africa. He recorded in Stockholm in March and in Stuttgart in April, and at a concert in Ljubljana, Yugoslavia (a live recording from May 10 was later issued), he improvised "Blues for Charlie Parker," which became his best-known composition. That year he also made an album in Johannesburg with a quartet and a group of penny-whistle players. In 1959 he left New York and the United States for a time, working in Helsinki that November, and through the 1960s he toured South, East and Southeast Asia. In spring 1962 he was recorded live in Hong Kong with a band that included the Italian saxophonist Giancarlo Barigozzi, and Japanese readers of DownBeat named him best clarinetist in 1960. In February 1964, in Japan, he recorded Music for Zen Meditation for Verve with Hōzan Yamamoto on shakuhachi and Shinichi Yuize on koto, a mostly improvised session often cited as the first new-age record. He played the Newport Jazz Festival in 1965, made Djanger Bali with the Indonesian All Stars in the Black Forest in October 1967, and followed the Zen album with Music for Yoga Meditation and Other Joys (1968, with sitar player Collin Walcott) and Music for Voodoo Meditation (1972).

He settled in Rome in 1970 and became a fixture of Italian jazz. He formed a five-year musical association with the pianist Romano Mussolini, with whom he made a self-produced duo album in 1973, and in the 1970s he worked with Marcello Rosa's ensemble on Friendship (recorded in June 1974), with guitarist Franco Cerri on a privately issued album, and in Prague with the Traditional Jazz Studio and with Jiří Stivín and Rudolf Dašek. He appeared as a Sicilian-American mob boss in Glauber Rocha's 1975 film Claro, made Prism (1977) for Polydor in the Netherlands with guitarist Jan Akkerman, and later made African Bird (Soul Note, 1984), Lush Life (Core, recorded 1981 to 1984, with guitarist Bill Frisell and bassist Ed Schuller), and in the 1990s a run of duo and trio albums with Italian pianists including Franco D'Andrea, Renato Sellani and Mario Rusca. In 2002 King Britt remixed his "Hare Krishna" for Verve's Verve Remixed, and in February 2006 he recorded A Jazz Life in Milan with five younger American players, among them tenor saxophonist Ben Wendel.

Scott passed away at his home in Rome on March 28, 2007, of prostate cancer, at 85. He was survived by his wife, Cinzia, and two daughters from earlier marriages. Franco Maresco's 2010 documentary Io sono Tony Scott is about his life, and the Italian clarinetist Francesco Bearzatti wrote the album Portrait of Tony for the centenary of his birth in 2021.

Scott came out of the bebop clarinet that Charlie Parker's example made possible, and at his peak in the 1940s and 1950s he was considered the most advanced clarinetist of his generation, with only Buddy DeFranco as a rival. He was heard as the cooler of the two: where DeFranco played a harder-driving bebop, Scott's tone and lines leaned toward the cool-jazz side. He was also an arranger and composer who wrote for large and small bands, and he was one of the first jazz players to take seriously the music he met on his travels: the shakuhachi and koto of Japan, the Indian sitar, Indonesian ensembles, African penny-whistle and tribal music. He stayed comparatively little known, since the clarinet had been in eclipse in jazz since the arrival of bebop, but his Zen and yoga meditation records came to be seen as forerunners of new-age and world-fusion music, and Four Tet sampled one of the Zen tracks on his 2001 album Pause. Scott cultivated an eccentric image, with a chest-length white beard and a stage routine in which he took his clarinet apart and used a section as a telephone, yet he kept playing at a high level into his 80s. In Italy he passed his approach on to younger players, most visibly the violinist Emanuele Parrini, who regarded him as a mentor and made a 2006 album in his honor on which Scott himself plays.