Andrew Hill was born June 30, 1931, in Chicago, Illinois, to William and Hattie Hill. His birth details were murky for decades: during his lifetime his year of birth was commonly given as 1937, and in the early 1960s he told people he had been born in Port-au-Prince, Haiti, apparently to seem more exotic to prospective employers and audiences. The Chicago birth date and birthplace were confirmed by his family in the announcement of his death and are now the figures used by Discogs, AllMusic, and the National Endowment for the Arts. He had a brother, Robert, a singer and classical violinist. As a boy Hill sang, played accordion, and tap-danced in local talent shows at Chicago's Regal Theatre between 1943 and 1947, and sold copies of the Chicago Defender, which sponsored some of those shows. He took up piano around age thirteen, encouraged by pianist Earl Hines, and attended the University of Chicago's Laboratory (Experimental) School. Composer Bill Russo introduced the teenaged Hill to classical composer Paul Hindemith, with whom he studied informally from 1950 to 1952. In 1950 he learned his first blues changes from saxophonist Pat Patrick, and as a teenager he gigged with touring musicians passing through the Midwest, including Charlie Parker and Miles Davis.

Hill played his first professional job in 1953 with saxophonist Paul Williams's band, doubling on baritone saxophone and piano, and first recorded as a sideman in 1954. In 1955 or 1956 (sources disagree on the exact year) he recorded a trio session with bassist Malachi Favors and drummer James Slaughter, released in 1960 as So in Love with the Sound of Andrew Hill on the Warwick label. After touring as an accompanist for Dinah Washington, Hill settled in New York City in 1961, working with vocalists Johnny Hartman and Al Hibbler. He then moved briefly to Los Angeles, playing in Roland Kirk's quartet and at the Lighthouse Café in Hermosa Beach, where he met organist Laverne Gillette, whom he married in 1963 after both had relocated to New York.

Back in New York, Hill's reputation was made by a run of Blue Note albums as leader, cut in barely two years: Black Fire (recorded November 1963, his label debut, with Joe Henderson, Richard Davis, and Roy Haynes), Smoke Stack (December 1963), Judgment! (January 1964, with Bobby Hutcherson and Elvin Jones), and Point of Departure (March 1964), a sextet session with Eric Dolphy, Joe Henderson, Kenny Dorham, Richard Davis, and Tony Williams that is widely regarded as his masterpiece and one of Blue Note's most ambitious dates of the era. He continued with Andrew!!! (June 1964) and Compulsion!!!!! (October 1965), both featuring tenor saxophonist John Gilmore, and recorded further sessions that Blue Note shelved for years or decades: a March 1966 date issued in part under Sam Rivers's name as Involution and not released complete as Change until 2007; Grass Roots (1968), with trumpeter Lee Morgan and Woody Shaw among the horns; Dance with Death (recorded 1968, unissued until 1980); Lift Every Voice (1969-70, with a wordless vocal chorus added to the small group); and the large-ensemble Passing Ships (recorded November 1969 with Dizzy Reece, Woody Shaw, Julian Priester, Joe Farrell, Howard Johnson, Robert Northern, Ron Carter, and Lenny White), which sat in the Blue Note vaults until Michael Cuscuna produced its release in 2003. Hill rarely worked as a sideman after the 1960s, preferring to lead his own dates, which limited his broader public exposure even as musicians and critics recognized his significance.

Through the 1970s Hill supported himself partly by teaching in California public schools and prisons while continuing to record prolifically for smaller labels: SteepleChase (Invitation, 1974; Divine Revelation, 1975), Freedom (Spiral, 1974-75, with Lee Konitz and Barry Altschul), the Japanese label East Wind (Blue Black, Hommage, and Nefertiti, all 1975-76), and Artists House (the solo From California with Love, 1978). He later held a tenure-track faculty position at Portland State University from 1989 to 1996, where he established the school's Summer Jazz Intensive program and also gave workshops and residencies at Wesleyan University, the University of Michigan, the University of Toronto, Harvard, and Bennington College. He returned briefly to Blue Note for Eternal Spirit (1989) and But Not Farewell (1990), both featuring alto saxophonist Greg Osby. Laverne Hill died in 1989 after a long illness; Hill married dancer and educator Joanne Robinson Hill in Portland in 1992, and the couple moved to New York City in 1995 and then to Jersey City, New Jersey, in 2000.

Hill's final decade brought a wave of renewed attention. In 1998 he formed a new Point of Departure Sextet, with Marty Ehrlich, Greg Tardy, Ron Horton, Scott Colley, and Billy Drummond, for the Knitting Factory's Texaco Jazz Festival, and in 2000 Palmetto Records released Dusk, a song cycle inspired by Jean Toomer's 1923 book Cane that was named album of the year by both DownBeat and JazzTimes. In 2003 Hill received the Jazzpar Prize, the Danish jazz award that came with a commissioned work for an assembled European ensemble, documented on the live album The Day the World Stood Still. Blue Note brought him back to the label a final time for Time Lines (recorded 2005, released February 2006), reuniting him with trumpeter Charles Tolliver; the album won DownBeat's Critics Poll for Jazz Album of the Year. According to critic and friend Howard Mandel, Hill was named the Jazz Journalists Association's Composer of the Year four times, most recently in 2006, and was among the first recipients of a Doris Duke Foundation award for jazz composers. On April 3, 2007, music publisher Boosey & Hawkes announced it had added Hill to its roster of composers. His final public performance came March 29, 2007, at Trinity Church in New York City. Andrew Hill passed away at his Jersey City home on April 20, 2007, at age 75, following a long battle with lung cancer. In May 2007 he became the first person to receive a posthumous honorary doctorate from Berklee College of Music; later that year DownBeat inducted him into its Jazz Hall of Fame via the Critics Poll, and in 2008 he was named an NEA Jazz Master, an honor his widow accepted on his behalf.

Hill's principal influences were pianists Thelonious Monk, Bud Powell, and Art Tatum; he described Monk's music as driven by "the personality of music," found Powell's vocabulary so total a model that copying it risked becoming a dead end, and called Tatum "the epitome of all modern piano playing." Where contemporaries like Cecil Taylor and Ornette Coleman were jettisoning bebop's harmonic and rhythmic scaffolding outright during the 1960s avant-garde upheaval, Hill worked from inside that scaffolding, extending rather than discarding it. His compositions were labyrinthine and rhythmically knotted without ever feeling aleatoric or arbitrary, and his own playing paired a flowing, elastic sense of time with a near-total avoidance of cliché. Because he rarely worked as a sideman after the 1960s and led an unusually independent, hard-to-categorize body of work, critic John Fordham noted that Hill's stature "remained largely inside knowledge in the jazz world for most of his career," even as musicians who came after him, including pianist Vijay Iyer, publicly credited him as a direct influence and mentor. Hill and Iyer became close in Hill's last years, and after Hill's death Iyer organized and led "Eternal Spirit: Vijay Iyer & Friends Celebrate the Music of Andrew Hill," a tribute concert at Harlem Stage in which his own program notes called Hill a "friend, mentor, and supporter."