Robert Edward Brookmeyer was born in Kansas City, Missouri on December 19, 1929, the only child of Elmer Edward Brookmeyer and Mayme Seifert. He began on clarinet at eight, and a performance by the Count Basie Orchestra at the Tower Theater was the thing that turned him toward jazz. At thirteen he worked all summer to buy a set of drums and came home to find himself installed as the sixth trombone player in the Central Junior High School band instead, which is how he ended up on the instrument at all. He was playing professionally with dance bands by fourteen and taught himself piano around sixteen. He spent three years at the Kansas City Conservatory of Music studying piano and composition, won the Carl Busch Prize for Choral Composition in 1949, and left without graduating for a job at the Aragon Ballroom in Chicago, where he played alongside Tiny Kahn, Al Cohn and Frank Rosolino.

After a brief spell in the US Army he moved to New York in 1952 and made his living as a freelance pianist who occasionally played trombone, working in the bands of Tex Beneke, Ray McKinley and Claude Thornhill, the orchestra whose book Gil Evans had written a few years earlier, and freelancing with Coleman Hawkins, Pee Wee Russell, Ben Webster, Charles Mingus and Teddy Charles. It was in the Thornhill band that he sold his slide trombone to another player and committed to the valve instrument, which almost nobody was using as a first horn. In 1953, playing in the Stan Getz Quintet, he won the DownBeat New Star Award for trombone. He left Getz in 1954 to join Gerry Mulligan, replacing Chet Baker in the pianoless quartet, and stayed with Mulligan's groups until 1957, appearing on the Paris concerts and the California and Storyville recordings that made his reputation. He then spent a year in the Jimmy Giuffre 3 with Jim Hall, a clarinet, guitar and valve trombone group with no piano and no drums that was among the first working bands to make free improvisation a regular part of a concert. In 1960 he rejoined Mulligan as chief arranger, composer and featured soloist of the Concert Jazz Band, a band he had helped form and which he wrote much of the book for through 1964. In the same years he made a two-piano album with Bill Evans, played on George Russell's New York, N.Y., arranged for Ray Charles and became one of the busiest studio players in New York.

In 1961 he and Clark Terry formed a quintet as co-leaders, a band that ran to 1967 and won both DownBeat and NARAS recognition, cutting Tonight, The Power of Positive Swinging and Gingerbread Men for Mainstream with Roger Kellaway and Hank Jones in the piano chair. In February 1965 the two men appeared together on BBC2's Jazz 625. That same year Brookmeyer became a founding member of the Thad Jones / Mel Lewis Jazz Orchestra, dividing his time between the lead trombone chair and the band's book. In April 1965 he also joined the house band of The Merv Griffin Show as a staff musician, work he found deeply unsatisfying.

In 1968 he moved to Los Angeles and became a full-time studio musician, playing sessions and staff arranging for film and television. He was almost entirely inactive as a jazz musician for the next decade, and he was open about why. He had been a heavy drinker since the 1950s and told the interviewer Jon Raney in February 2011 that by the late 1960s he was "almost not hire-able" in New York, that California was an attempt at a fresh start, and that he lasted about four years there as a functioning alcoholic before, in his phrase, it catches up with you. Getting sober took two stays in hospital: the first time, he said, he did nothing anyone asked of him, and the second time he did. During his first sober year he went to school for counselling in California for almost a year and seriously considered staying and working as an alcoholism counsellor rather than returning to music. He kept alcohol out of his house entirely for two or three years afterward, and he stayed sober for the rest of his life.

He came back in 1978. Back Again was cut in New York that May, the Brookmeyer Small Band played two nights at Sandy's Jazz Revival in Beverly, Massachusetts in July that produced a live double album, and he toured Europe with the Stan Getz sextet. The Getz band he rejoined had Billy Hart on drums, and Brookmeyer's account of it is that Hart pulled him aside in San Francisco to ask him to get Getz off his back. He also spent a year working exclusively in a duo with Jim Hall, a partnership documented on a Hague concert recording finally issued twenty years later. Then Thad Jones left for Copenhagen, Mel Lewis called, and in 1979 Brookmeyer became musical director of the reorganised Mel Lewis Jazz Orchestra. He had written nothing for a decade, and as he put it, the charts he began producing for Lewis were the first writing he had done since he was a recovered drunk. The results were Bob Brookmeyer: Composer and Arranger, taped at the Village Vanguard in 1980, and Make Me Smile and Other New Works by Bob Brookmeyer, taped there over five nights in January 1982. He received his first National Endowment for the Arts grant for jazz composition in 1980 and two more later.

From 1981 he worked increasingly in Europe as a composer and conductor, writing for the WDR Big Band in Cologne and the Stockholm Jazz Orchestra among others, and in the early 1980s he was mentored by the American experimental composer Earle Brown, with whom he worked through twentieth-century concert music in depth. Teaching became the other half of his life. He joined the faculty of the Manhattan School of Music in the late 1980s and directed the BMI Jazz Composers Workshop from 1989. In 1991 he moved to Rotterdam, organised the World School for New Jazz and taught composition and improvisation at the Rotterdam Conservatory; the University of Missouri-Kansas City gave him an honorary doctorate the same year. In 1994 he was appointed musical director of the Schleswig-Holstein Musik Festival Big Band, an eighteen-piece ensemble that evolved over the next few years into his own New Art Orchestra, the group that carried his writing for the rest of his life across New Works (Celebration), Waltzing with Zoe, Get Well Soon, Spirit Music and Standards. In 1996 he became artistic director of the composition workshop at the Rhythmic Conservatory in Copenhagen, and in 1997 he returned to the United States to teach full time at the New England Conservatory in Boston, where he chaired the department of jazz composition and created the school's Jazz Composers' Workshop Orchestra before retiring in 2007.

He joined ArtistShare in June 2005 and used it to fund Spirit Music, released in 2006, the year he was named a National Endowment for the Arts Jazz Master. The New England Conservatory awarded him an honorary doctorate in 2008. His last album, Standards, made with the New Art Orchestra and the Dutch singer Fay Claassen and carrying liner notes by Maria Schneider, was released on November 30, 2011. He passed away of congestive heart failure on December 15, 2011 in New London, New Hampshire, four days short of his eighty-second birthday, and was survived by his wife Janet. His papers, thirty-four linear feet of manuscripts, correspondence, photographs and recordings, were given by Janet Brookmeyer to the Ruth T. Watanabe Special Collections at the Eastman School of Music's Sibley Music Library in April 2015, where they remain the primary archive of his work.

Brookmeyer built a career on an instrument nobody else was making a career on: he played valve trombone as a first horn rather than a double, and said plainly that he set out to become a first, second and third trombone player on it because the valve instrument had a reputation for sounding bad and he wanted to disprove that. His playing had the dry, unhurried, slightly sardonic quality that the cool and West Coast schools are known for, and it worked in Gerry Mulligan's pianoless quartet and Jimmy Giuffre's pianoless, drummerless trio precisely because he could carry harmonic weight without a rhythm section under him. The writing is what he is now most consequential for, and it is unusual in jazz for how directly it imports twentieth-century concert technique into a big-band score: "ABC Blues" generates its melodies and harmonies from an atonal tone row, "The Big Time" develops earlier material through polytonality, and "Seesaw", "Silver Lining" and "Hello and Goodbye" run on chromatic harmony and tone clusters. He was mentored in that repertoire by the composer Earle Brown in the early 1980s, and named Witold Lutosławski, Igor Stravinsky, Claude Debussy, György Ligeti and Béla Bartók as the composers who shaped him; he used Lutosławski's cello concerto in the classroom to show students what could be built from a simple motif. The line of descent from him is unusually clear for a jazz composer. He told Jim McNeely to write for Mel Lewis's band and kept sending him back until a chart worked, then took him to Cologne. Maria Schneider studied with him between 1986 and 1991 on a National Endowment for the Arts grant and names him and Gil Evans as her two mentors. Kenny Werner was pushed into large-ensemble composition by him in the same Vanguard band. Oded Lev-Ari studied jazz composition under him at the New England Conservatory, and Ingrid Jensen names him among her teachers. Younger writers who never studied with him, Nick Finzer and Manuel Valera among them, name him alongside Gil Evans and Thad Jones when they are asked whose large-ensemble writing they came out of.