Anthony Delano Braxton was born June 4, 1945, in Chicago, Illinois, to Julia Samuels Braxton, from Tulsa, Oklahoma, and Clarence Dunbar Braxton Sr., from Greenville, Mississippi; he had three brothers, and his stepfather, Lawrence Fouche, worked for Ford Motor Company. He attended Betsy Ross Grammar School on Chicago's South Side and later studied at the Chicago School of Music from 1959 to 1963. He briefly attended Wilson Junior College before financial difficulties ended that path, then studied philosophy and music composition at Roosevelt University without completing a degree. In 1963 he joined the United States Army, playing saxophone in the Fifth Army Band, initially stationed near Chicago before a posting to South Korea with the Eighth Army Band; he was discharged in 1966.

Back in Chicago, Braxton joined the Association for the Advancement of Creative Musicians (AACM), the collective founded the previous year by Muhal Richard Abrams and colleagues, after meeting Roscoe Mitchell, who invited him to rehearse with and then join the group. In 1967 he formed the trio Creative Construction Company with violinist Leroy Jenkins and trumpeter Wadada Leo Smith (then recording as Leo Smith), and the following year he made his debut as a leader with Three Compositions of New Jazz (Delmark, 1968), featuring Jenkins, Smith, and Abrams. In 1969 he recorded For Alto, a solo double LP believed to be the first full-length recording for unaccompanied saxophone, released on Delmark in 1971. That same year he moved briefly to Paris, where he joined bassist Dave Holland, pianist Chick Corea, and drummer Barry Altschul in the collectively led quartet Circle, documented on ECM's Paris Concert (recorded February 21, 1971); the group disbanded within about a year, though Holland and Altschul continued to work in Braxton-led groups afterward. He also appeared as a sideman in this period on Marion Brown's ECM album Afternoon of a Georgia Faun (1970) and on Holland's own ECM debut as a leader, Conference of the Birds (recorded 1972), alongside Sam Rivers and Altschul.

Braxton relocated to New York in the early 1970s. He led a working quartet documented on Town Hall 1972 with Holland, Altschul, and reedman John Stubblefield, and cut two volumes of standards with pianist Tete Montoliu's trio for the Danish label SteepleChase, both titled In the Tradition (recorded 1974). Signing to the major label Arista, he spent roughly six years there producing some of his most acclaimed studio work: New York, Fall 1974, an octet date with Leroy Jenkins, Julius Hemphill, Hamiet Bluiett, Oliver Lake, and Kenny Wheeler; Five Pieces 1975, a quartet recording with Holland, Altschul, and Wheeler; Creative Orchestra Music 1976, a big-band album featuring Abrams and Roscoe Mitchell as fellow soloists and George Lewis and Wadada Leo Smith among the personnel; Duets 1976, a full duo record with Abrams; and Alto Saxophone Improvisations 1979, a second unaccompanied solo statement. In 1978 he recorded the duo album Birth and Rebirth with drummer Max Roach for the Italian label Black Saint.

The early-to-mid 1980s brought the ensemble most identified with Braxton's small-group work: a quartet formed around pianist Marilyn Crispell, initially with bassist John Lindberg and drummer Gerry Hemingway on Six Compositions (Quartet) 1984 (Black Saint), and from 1985 on with bassist Mark Dresser in Lindberg's place, documented extensively on the Leo Records box Quartet (London) 1985 and on the standards-repertoire sessions Seven Standards 1985, Volumes I and II. The same period produced Composition 98 (hatART, 1981) with Crispell, trombonist Ray Anderson, and trumpeter Hugh Ragin, and, later in the decade, Eight (+3) Tristano Compositions, 1989: For Warne Marsh, a tribute session with bassist Cecil McBee and drummer Andrew Cyrille. From 1985 to 1990 Braxton taught at Mills College in Oakland, California, and in 1990 he joined the faculty of Wesleyan University in Middletown, Connecticut, where he remained until his retirement at the end of 2013, ultimately holding the title John Spencer Camp Professor of Music, Emeritus.

In 1994 Braxton received a MacArthur Fellowship, which helped finance large-scale projects he had long envisioned, including an opera cycle. He founded his own Braxton House label (later New Braxton House) and revived the nonprofit Tri-Centric Foundation to support his archive and other creative artists. Through the 1990s and 2000s he developed Ghost Trance Music, a body of roughly 150 compositions written between 1995 and 2006 and inspired partly by the Native American Ghost Dance, alongside earlier and later compositional systems including Language Music, Diamond Curtain Wall, and Falling River Music. His Trillium opera project produced multiple full-length works, including Trillium R (composed and recorded 1996, released on Braxton House in 1999) and, after his Wesleyan retirement, the five-act Trillium J (recorded and filmed in 2014, released in 2016), both drawing on large casts of vocalists, dancers, and the Tri-Centric Orchestra. He also produced smaller archival milestones such as Wesleyan (12 Altosolos) 1992, a third unaccompanied-alto recording, and Anthony Braxton's Charlie Parker Project 1993, a tribute session recorded in Zurich and Cologne with Joe Fonda, Han Bennink, Misha Mengelberg, and others.

In the 21st century Braxton continued to record prolifically, both new studio and concert work and an ongoing series of archival releases documenting decades of previously unissued performances. Later landmark recordings include 9 Compositions (Iridium) 2006, a boxed 12+1tet set on Firehouse 12 built around the final compositions of the Ghost Trance cycle, with longtime collaborators Taylor Ho Bynum, Mary Halvorson, and Nicole Mitchell; Echo Echo Mirror House (NYC) 2011, in which ensemble members played compositions sampled onto iPods alongside live performance; and Quartet (New Haven) 2014, a 2019 Firehouse 12 release pairing Bynum with guitarist Nels Cline and drummer Greg Saunier of Deerhoof. He received the Doris Duke Performing Artist Award in 2013 and was named a 2014 NEA Jazz Master, and he holds honorary doctorates from the University of Liège (2009) and the New England Conservatory (2016); a 1981 Guggenheim Fellowship and a 2020 United States Artists Fellowship also number among his honors. He is the father of Tyondai Braxton, formerly of the band Battles.

Braxton's music sits at the intersection of the AACM's collective, self-composed creative-music tradition and a lifelong engagement with jazz's inside vocabulary: he has repeatedly named cool-toned altoist Paul Desmond and, especially, Warne Marsh and the Lennie Tristano school as formative influences on his own alto playing, alongside John Coltrane, and paid tribute to both Tristano and Thelonious Monk directly on record. Rather than titling most of his compositions with words, he identifies them by number and by graphic or diagrammatic notation, and across his career he built a series of distinct notational and conceptual systems, Language Music, Ghost Trance Music, Diamond Curtain Wall, and Falling River Music among them, that let notated structure and free improvisation coexist within the same piece. He is a strikingly versatile multi-instrumentalist, moving across the entire saxophone family from sopranino to contrabass plus the clarinet family and piano, and equally at home leading a solo recital, a working small group, or a full orchestra. That range, combined with a body of work numbering in the hundreds of recordings, has made him one of the most influential and most discussed figures to emerge from the post-Coleman, post-Coltrane creative-music movement, cited by critics and later generations of improvisers as a central bridge between jazz's improvisational tradition and 20th-century concert-music composition.