James Edward Heath was born in Philadelphia on October 25, 1926, the middle of three musical brothers. His father was an auto mechanic who played clarinet on weekends, his mother sang in a church choir, and his sister played piano. The older brother, Percy, became one of the most recorded bassists in jazz and spent four decades in the Modern Jazz Quartet; the youngest, Albert "Tootie" Heath, became a first-call drummer. Jimmy grew up in South Philadelphia and got his first alto saxophone at Christmas 1941. He was rejected for the wartime draft for falling under the minimum weight, which left him free to work: from late 1945 through most of 1946 he toured with the Nat Towles band out of Omaha, his first professional job.

Back in Philadelphia in 1946 he put together a big band that held the city's scene for three years and turned out to be one of the great uncredited proving grounds of postwar jazz. The saxophone section included John Coltrane on second alto and Benny Golson; the rest of the band drew on Cal Massey, Johnny Coles, Ray Bryant, Nelson Boyd and drummer Specs Wright. Charlie Parker and Max Roach sat in with it on one occasion, and the band played rooms as far afield as the Apollo Theater in Harlem. Almost nothing survives of it: Heath recalled cutting a few acetate demos that were never released, and the book of arrangements was lost at a Chicago train station. In 1948 he worked with trumpeter Howard McGhee, including an appearance at the first International Jazz Festival in Paris at the Salle Pleyel on a bill that also carried Coleman Hawkins and Erroll Garner. It was in the McGhee and Dizzy Gillespie bands that his Parker-saturated alto playing earned him the nickname "Little Bird," a tag that fit his five-foot-three frame as neatly as his phrasing. He broke up the Philadelphia band in 1949 to join Gillespie's orchestra, and stayed on into the smaller group Gillespie kept working when the big band folded, alongside Coltrane, Milt Jackson and his own brother Percy.

Heath moved to tenor saxophone in the early 1950s, partly to get out from under the Parker comparison, and the horn suited him. In 1953 he turned up on two sessions that still get played: Miles Davis's April 20 Blue Note date with J.J. Johnson, Gil Coggins, Percy Heath and Art Blakey, which produced the first recording of Heath's tune "C.T.A.," and a June session under Johnson's name with Clifford Brown, John Lewis, Percy Heath and Kenny Clarke. Then the career stopped. Heath was a heroin addict, and he was arrested and convicted twice for selling. The first arrest, in the spring of 1954, sent him to the Federal Medical Center at Lexington, Kentucky. Arrested again in early 1955, he was sentenced to six years and served most of it at Lewisburg Penitentiary in Pennsylvania. He came off heroin there for good, took up the flute, ran the prison big band and wrote steadily, sending scores out through his brother Tootie. Five of the pieces on Chet Baker and Art Pepper's Playboys were written by Heath while he was inside. He was released early, on May 21, 1959, and stayed clean for the rest of his life.

The comeback was immediate but hemmed in. Miles Davis hired him in 1959 to replace Coltrane, but the terms of Heath's parole restricted his travel and the job could not last. What did last was a contract with Riverside and a producer, Orrin Keepnews, who let him write. Between September 1959 and the spring of 1964 Heath cut six albums for the label, and their most striking feature is how little they sound like blowing dates. The Thumper (1959) is a straight sextet with Nat Adderley, Curtis Fuller, Wynton Kelly, Paul Chambers and Albert Heath. After that he kept enlarging and recoloring the ensemble: Really Big! (1960) is a ten-piece with French horn, baritone saxophone and both Adderley brothers; The Quota (1961) and Triple Threat (1962) build a sextet around Freddie Hubbard, Julius Watkins's French horn and Cedar Walton, with Percy and Albert as the rhythm section; Swamp Seed (1963) adds tuba, a second French horn and two pianists, Herbie Hancock and Harold Mabern. Alongside the leader dates he became one of the most heavily used tenor players in New York, working with Milt Jackson and Art Farmer through most of the 1960s and recording with Kenny Dorham, Blue Mitchell, Sam Jones, Elmo Hope, Julian Priester, Donald Byrd and Gil Evans.

The 1970s pushed him in two directions at once. He started teaching, first through Billy Taylor's Jazzmobile in Harlem, and he began writing long form: the multi-movement Afro-American Suite of Evolution, commissioned by Jazzmobile and scored for a thirty-piece orchestra, premiered at New York's Town Hall. His own records got looser and more electric, from The Gap Sealer (Cobblestone, 1972, with his son James Mtume on percussion) through Love and Understanding (Muse, 1973) to the acoustic quartet date Picture of Heath (Xanadu, 1975) with Barry Harris, Sam Jones and Billy Higgins, which collected five of his best-known originals on one record. In 1975 the three brothers finally formed a permanent band. The Heath Brothers, with pianist Stanley Cowell as the fourth member, recorded Marchin' On! for Strata-East, moved to Columbia for four albums between 1978 and 1981, and then to Antilles. Percy stepped back from the group in the early 1980s, Tony Purrone's guitar became a fixture, and the band worked on and off for the next thirty years.

Heath's later career was as much about the classroom as the bandstand. He joined the faculty of the Aaron Copland School of Music at Queens College, City University of New York, in 1987 to help build a new master's program in jazz, and taught there until 1998, drawing Donald Byrd and others to the campus and serving on the board of the Louis Armstrong Archives. He also kept recording: two more albums for Orrin Keepnews at Landmark, New Picture (1985) and Peer Pleasure (1987); two quartet dates for SteepleChase; and Little Man Big Band (Verve, 1992), which put his own arrangements in front of an eighteen-piece band with Roland Hanna and Lewis Nash. From there the Jimmy Heath Big Band became his main large-ensemble outlet, documented on Turn Up the Heath (2004 and 2006 sessions, with Slide Hampton, Antonio Hart, Peter Washington and Lewis Nash) and on Togetherness, recorded live at the Blue Note in October 2011. He was named an NEA Jazz Master in 2003, the year after Percy received the same honor, and published his autobiography, I Walked With Giants, written with Joseph McLaren, in 2010. His last record was made in two sessions in late 2019, at Sear Sound in New York and 800 East Studios in Atlanta: Love Letter, a ballad program with Kenny Barron, Russell Malone, David Wong and Lewis Nash, plus guest appearances by Cécile McLorin Salvant, Gregory Porter and Wynton Marsalis. Heath passed away of natural causes in Loganville, Georgia, on January 19, 2020, at 93. Verve released Love Letter six months later.

Heath started as one of the most convincing Charlie Parker disciples on alto and spent the rest of his life proving he was more than that. On tenor he settled into a dry, compact, hard-swinging sound with none of the vibrato-heavy weight of the Coleman Hawkins line and none of the sheets of sound his old sectionmate John Coltrane was building at the same time. He played short, and he wrote long. The writing is where his influence actually sits: "C.T.A.," first cut by Miles Davis in 1953, and "Gingerbread Boy," which Davis recorded again on Miles Smiles in 1966, both entered the standard repertoire, and "For Minors Only," "Big P," "Mona's Mood" and "The Voice of the Saxophone" have been taken up by players from Art Farmer and Chet Baker to Cannonball Adderley, Clark Terry, James Moody, Milt Jackson, Ray Charles, Dizzy Gillespie and Dexter Gordon. As an arranger he had a specific and unusual taste in ensemble color, reaching repeatedly for French horn, tuba and baritone saxophone to thicken a small group into something orchestral without turning it into a big band: Really Big!, The Quota and Swamp Seed are all built that way. He wrote more than 125 pieces and appeared on well over a hundred albums, and by the end of his life the students who came through Queens College and Jazzmobile were as much a part of the legacy as the records.