Scott Hamilton was born on September 12, 1954, in Providence, Rhode Island. He heard jazz early through his father's large record collection and tried several instruments as a child: drums at about five, piano at six, harmonica, and a few clarinet lessons around age eight, which remained the only formal instruction he ever had. Even then he was drawn to the sound of Johnny Hodges, and he began playing the saxophone seriously at about sixteen. His first band, the Hamilton-Bates Blue Flames, was a Providence blues and jazz group built around the guitarist Fred Bates, with Hamilton on harmonica and alto saxophone. When the drummer Chuck Riggs joined in 1972 and Hamilton switched to tenor, the music moved toward swing and the band became the Scott Hamilton Quartet.

In 1975 he played in Boston with the trumpeter Roy Eldridge, who became his champion, and in 1976, at twenty-two, he moved to New York City. Eldridge's recommendation led to a six-week engagement at Michael's Pub, and the city still had veterans at work: Hamilton played with Hank Jones and Anita O'Day and learned from Illinois Jacquet, Vic Dickenson and Jo Jones. The pianist John Bunch arranged his first recording date, for the Famous Door label in December 1976, and brought him into the band of Benny Goodman, with whom he worked on and off until the early 1980s.

In 1977 he recorded for Chiaroscuro with Bob Wilber, and that year Carl Jefferson of Concord Jazz heard him and began recording him. His first Concord album, Scott Hamilton Is a Good Wind Who Is Blowing Us No Ill (1977), paired him with the trumpeter Bill Berry, the pianist Nat Pierce, the bassist Monty Budwig and the drummer Jake Hanna. Concord kept him recording for more than three decades, as a leader, as a member of the Concord Jazz All Stars, and in a run of co-billed dates: two albums with the cornetist Warren Vaché (1978 and 1980), two with the tenor saxophonist Buddy Tate (1979 and 1981), No Bass Hit (1979) and Major League (1986) with the pianist Dave McKenna and the drummer Jake Hanna, Tour de Force (1982) with Al Cohn, two with the cornetist Ruby Braff (1985 and 1986), and A Sound Investment (1987) with Flip Phillips. He was also the regular tenor saxophonist on Rosemary Clooney's Concord albums, from Everything's Coming Up Rosie (1977) to Do You Miss New York? (1993), and accompanied her on the road. In January 1986 he recorded Soft Lights & Sweet Music with Gerry Mulligan, an album that earned him a Grammy nomination.

Through the 1980s he toured Japan, Sweden and the United Kingdom and played the Grande Parade du Jazz in Nice, France. His quintet's live album The Second Set was taped at Yamaha Hall in Tokyo in June 1983. He first played in London in 1978 and had residencies with Braff at the Pizza Express Jazz Club there in the mid-1980s. In the 1990s he moved to London, where he formed a quartet with the pianist John Pearce, the bassist Dave Green and the drummer Steve Brown. By 2008 he was one of the patrons of the Brecon Jazz Festival in Wales, where in 2007 he had guested with Humphrey Lyttelton's band, a performance partly shown on BBC Four as Humph's Last Stand after Lyttelton's death in 2008. The inaugural Ronnie Scott's Jazz Awards in 2007 named him International Jazz Saxophonist of the Year.

In the late 2000s Hamilton settled in Tuscany, Italy, and has toured from there across Europe, Japan and the United States. His Concord years closed with Nocturnes & Serenades (2006) and Across the Tracks (2008), and the albums since have come from independent labels: Midnight at Nola's Penthouse (Arbors, 2010) with the pianist Rossano Sportiello, 'Round Midnight (Challenge, 2012) with Harry Allen, duo albums with the pianist Andrea Pozza in 2013 and 2015, and, from 2015, a series for the Italian label Fonè Jazz with a quartet that includes the pianist Paolo Birro. He worked in Spain with the singer Andrea Motis and the bandleader Joan Chamorro in 2013, 2014, 2018 and 2021, and recorded with the Swedish pianist Jan Lundgren and the Norwegian singer Karin Krog on The Best Things in Life (2016). The Rhode Island Music Hall of Fame inducted him in its jazz category in 2020. His most recent albums are Looking Back (Stunt, 2024) and In the Still of the Night (GLM, 2026), a quintet date with the vibraphonist Tizian Jost.

Hamilton plays in the swing tenor tradition of Ben Webster, Coleman Hawkins and Zoot Sims, with a broad, warm tone, relaxed phrasing and an unhurried command of ballads and medium-tempo standards. He arrived in the mid-1970s, when fusion dominated, as a young player committed to the pre-bop mainstream, and within the swing revival he came to be seen as its future. The sound of Johnny Hodges was his earliest attraction, and Roy Eldridge, the older trumpeter who sponsored him, was a candid critic whose standards he has said he valued. The British critic Dave Gelly compared a Hamilton solo to listening to a fluent conversationalist: a recognizable sound first, then an informal style and an easy command of the jazz language. Critics often pair him with Harry Allen, a younger tenor saxophonist who first sat in with him as a teenager at Newport and later recorded two twin-tenor albums with him. His repertoire stays close to the American songbook, Duke Ellington and the blues.