Donald Johnson Ellis was born on July 25, 1934, in Los Angeles, the son of a Methodist minister and a church organist. He went to West High School in Minneapolis, where a Tommy Dorsey big band concert first drew him toward jazz, with Louis Armstrong and Dizzy Gillespie as early inspirations, and he took a music composition degree at Boston University in 1956. His first professional job was with the Glenn Miller orchestra, then directed by Ray McKinley. He left it in September 1956 for the U.S. Army's Seventh Army Symphony Orchestra and Soldiers' Show Company, posted to Frankfurt, Germany, where he met the pianist Cedar Walton and the saxophonists Eddie Harris and Don Menza and wrote for a big band for the first time.

After two years he left the Army band and moved to Greenwich Village, where the work was mostly dance bands and local jobs. He toured briefly with Charlie Barnet and in spring 1959 joined Maynard Ferguson's band for nine months. From there he moved into New York's avant-garde. He recorded with Charles Mingus and spent two years in George Russell's sextet, which made Ezz-thetics (1961), with Eric Dolphy in the front line, and The Outer View (1962). Under his own name he led small-group dates between 1960 and 1962 with players including Jaki Byard, Paul Bley, Gary Peacock, Ron Carter, Charlie Persip and Steve Swallow, ending with Essence in mid-July 1962. On June 3, 1962 he took part in Edgar Summerlin's jazz liturgy Evensong at the First International Jazz Festival in Washington, D.C., with Dolphy, Slide Hampton, Carter and Persip in the ensemble. That October he went to Poland for the Warsaw Jazz Jamboree, where his quartet was partly recorded for a Polish release, and wrote up the trip for Down Beat as "Warsaw Diary" (January 3, 1963). He also played the NDR Jazz Workshop in Hamburg that December, spent early 1963 in Stockholm staging happenings, and on February 10, 1963 launched the Improvisational Workshop Orchestra at the Five Spot in New York, a band that let performers choose events from cards and interpret a painter's work.

In 1964 Ellis began graduate studies in ethnomusicology at UCLA, where the Indian musician Harihar Rao became his teacher. Together they wrote "An Introduction to Indian Music for the Jazz Musician" (1965), and Ellis set out to bring odd meters into Western improvisation. A Rockefeller grant to work at SUNY Buffalo for a year interrupted an early version of his big band, and while in New York he also took part in Third Stream projects: a February 8, 1964 Lincoln Center performance filmed for Leonard Bernstein's Young People's Concerts, and, with the New York Philharmonic, Larry Austin's "Improvisations for Orchestra and Jazz Soloists" and Gunther Schuller's "Journey Into Jazz." His first symphony, "Contrasts for Two Orchestras and Trumpet," was premiered by the Los Angeles Philharmonic under Zubin Mehta in November 1967. Back in California he formed the Hindustani Jazz Sextet with Rao on sitar and tabla and the vibraphonist Emil Richards, generally regarded as the first band of its kind in the United States. It performed "Synthesis," a piece by Ellis, with Stan Kenton's Neophonic Orchestra at the Los Angeles Music Center in February 1966 and opened for the Grateful Dead and Big Brother and the Holding Company at the Fillmore Auditorium on July 14 of that year.

Meanwhile a rehearsal band of his own played Monday nights, first at Club Havana and then at Bonesville in Hollywood, charging a small admission, and a letter-writing campaign won it a place at the 1966 Monterey Jazz Festival. Ellis had received a Holton trumpet with a fourth valve in September 1965 that let him play quarter tones, and the orchestra pushed far past the usual meters, writing in 5/4, 7/8 and 9/4 and then in 19/8 and 27/16. On September 18, 1966 it drew a standing ovation after its first piece, "33 222 1 222," a figure in 19, and went on to play pieces in 7, 9 and 27. Pacific Jazz issued the festival recording in 1967 as 'Live' at Monterey!, followed by Live in 3 2/3/4 Time from the Pacific Jazz Festival (October 1966) and Shelly's Manne-Hole (March 1967).

Producer John Hammond signed the band to Columbia, and Electric Bath was recorded in September 1967. Released in 1968, it was a Grammy nominee and won the Down Beat readers poll for album of the year; "Open Beauty" featured Ellis's trumpet run through an Echoplex. Shock Treatment was recorded in February 1968, followed by Autumn (1968), which carries the twenty-minute "Variations for Trumpet" and "Pussy Wiggle Stomp," and The New Don Ellis Band Goes Underground (1969), with the singer Patti Allen and pop and rock arrangements. Three nights at Bill Graham's Fillmore West in June 1970 became the double LP Don Ellis at Fillmore. In May 1971 Ellis added a string quartet and hired the Bulgarian pianist Milcho Leviev, who stayed five years; the band was recorded that month at Basin Street West in San Francisco for the double album Tears of Joy, which includes "Strawberry Soup," a piece that has been the subject of doctoral dissertations. William Friedkin asked him to score The French Connection (1971), which Ellis wrote for his own orchestra, and his arrangement of its theme won the Grammy for Best Instrumental Arrangement at the 15th annual awards in 1973. He later scored Kansas City Bomber (1972), The Seven-Ups (1973) and French Connection II (1975), and the 1969 film Moon Zero Two carries a score credited to Ellis and Philip Martell. His last Columbia album, Connection (August 1972), set pop songs by Carole King, Yes, Andrew Lloyd Webber and the Carpenters, often in odd meters, beside the film theme and Hank Levy's "Chain Reaction."

In 1973 Ellis recorded Soaring with the orchestra for MPS, with Levy's "Whiplash" and Leviev's "Sladka Pitka," and then Haiku, ten pieces based on Japanese haiku with a core quintet that included Ray Brown and the drummer John Guerin, backed by a string orchestra. In 1974 Ellis toured with the Organic Band, a leaner group with no electronics apart from amplification and a vocal quartet, and began studying Brazilian music. Heart trouble then stopped him: after a series of diagnoses that ended in cardiomyopathy, he went into ventricular fibrillation in May 1975 and survived. He was working again by 1976, and on December 3 the orchestra appeared on a Shirley MacLaine television special, playing his arrangement of "Sweet Georgia Brown" with a solo by Art Pepper. Signed to Atlantic in 1977, he recorded two Star Wars themes for a single and the album Music from Other Galaxies and Planets in a rush, then took the orchestra to the Montreux Jazz Festival, which produced Live at Montreux (1978), his last album as a leader. His last known public performance was on April 21, 1978, at the Westside Room in Century City, after which his doctor told him to stop touring and playing trumpet. On December 17, 1978, after attending a concert by Jon Hendricks, Ellis suffered a fatal heart attack at his North Hollywood home. He was 44 and is buried at Forest Lawn Memorial Park in the Hollywood Hills. He also wrote two books, The New Rhythm Book (1972) and Quarter Tones (1975), and his papers, instruments and Grammy are held in the Don Ellis Collection at the UCLA Ethnomusicology Archive.

Ellis's music joined three things that rarely shared a stage: the rhythmic cycles he studied with Harihar Rao, which he turned into big-band writing in meters such as 7/8, 19/8 and 27/16 and later in Bulgarian and Greek folk rhythms; the avant-garde and Third Stream ideas of his New York years, including the quarter-tone trumpet and experiments with chance and happenings; and, from 1967, electronics and rock. His orchestra was built to match: two drum sets, three double basses, extra percussion, piano and organ at first, then a single electric bass, a string quartet from 1971 amplified with Barcus-Berry pickups, an Echoplex and a ring modulator built for him by Tom Oberheim. In his last years he added the superbone and the firebird, valve instruments that combine trombone and trumpet qualities. His trumpet playing was technically formidable: The Guardian's John Fordham described a sound that joined technical command with classical clarity and old-school brass bravado, even on the strings-backed Haiku. Critical reception has been warm toward the early small-group dates (Down Beat's Pete Welding gave New Ideas five stars in 1962) and toward Electric Bath, Autumn and Tears of Joy, more mixed toward the pop-oriented Connection and The New Don Ellis Band Goes Underground, and sharply negative toward the hurriedly assembled Music from Other Galaxies and Planets. His influence ran through his sidemen and through school bands: Tom Scott, John Klemmer, the trombonist Glenn Ferris and Milcho Leviev went on to careers of their own, while his published charts were taken up by high school and college big bands, Hank Levy's "Whiplash," first recorded by the orchestra, later gave a 2014 film its title, and his books The New Rhythm Book and Quarter Tones set out methods for practising unusual meters and quarter-tone playing.