David Warren Brubeck was born on December 6, 1920, in Concord, California, and grew up in the rural town of Ione, where his father, Peter Howard Brubeck, ran cattle. His mother, Elizabeth, had studied piano in England with Myra Hess and gave him his first lessons; he could not read music well as a child, which he blamed on poor eyesight, and he got by on his ear. His older brothers Henry and Howard were already headed for music. Brubeck entered the College of the Pacific in Stockton in 1938 to study veterinary science, switched to music at the urging of the head of zoology, and was nearly expelled when a professor found out he could not sight-read, until other faculty vouched for his counterpoint and harmony. He was allowed to graduate in 1942 on the promise that he would never teach. That September he married Iola Whitlock, a fellow student.

Drafted after graduation, he served in Europe with the Third Army under George S. Patton. He volunteered to play piano at a Red Cross show that went over so well he was kept out of combat, and he led the Wolfpack, one of the first racially integrated bands in the American armed forces. In 1944 he met the alto saxophonist Paul Desmond. After nearly four years in uniform he enrolled at Mills College in Oakland and studied with the composer Darius Milhaud, who pushed him toward fugue and orchestration rather than classical piano; he had also taken two lessons from Arnold Schoenberg at UCLA while still on active duty, which ended badly because Schoenberg wanted every note accounted for. From the Milhaud circle came the Dave Brubeck Octet, which recorded between 1946 and 1950 with Desmond, the clarinetist William O. Smith, the tenor saxophonist David Van Kriedt and the drummer and vibraphonist Cal Tjader, and a trio with Tjader and the bassist Ron Crotty. In 1949 the San Francisco label owner Jack Sheedy, unable to pay his bills, handed his masters to the Circle Record Company, whose owners Max and Sol Weiss renamed their business Fantasy Records; the first Brubeck records sold 40,000 to 50,000 copies a quarter.

In 1951 he formed the Dave Brubeck Quartet around Desmond and took up a residency at the Black Hawk in San Francisco. The group toured college campuses and recorded there: Jazz at Oberlin was taped on March 2, 1953, at Finney Chapel at Oberlin College, and Jazz at the College of the Pacific on December 14, 1953. Believing he owned a stake in Fantasy, Brubeck worked as a scout for the label and urged the Weisses to sign Gerry Mulligan, Chet Baker and Red Norvo; when he found the deal gave him only half of his own recordings, he left for Columbia in 1954. Jazz Goes to College, assembled from concerts at the University of Michigan, the University of Cincinnati and Oberlin, was among his first Columbia releases, and in November 1954 he became the second jazz musician on the cover of Time, after Louis Armstrong in February 1949. He found the honor embarrassing and thought Duke Ellington more deserving; when Ellington knocked on his hotel door to show him the cover, Brubeck told him it should have been him. The rhythm section changed often in these years, with Crotty, Bob Bates and Norman Bates on bass and Lloyd Davis and Joe Dodge on drums, until the drummer Joe Morello, formerly with Marian McPartland, joined in 1956. The bassist Eugene Wright came aboard for the quartet's 1958 State Department tour of Poland, Turkey, India, Ceylon, Pakistan, Iran and Iraq and became a permanent member in 1959. Brubeck reportedly canceled concerts and a television appearance when hosts objected to presenting an integrated band, and in January 1960 he called off a 25-date tour of Southern colleges after 22 of the schools refused to let Wright perform.

Time Out was recorded at Columbia's 30th Street Studio in New York on June 25, July 1 and August 18, 1959, with Teo Macero producing. It was built on the odd meters the quartet had heard on its 1958 tour: "Blue Rondo à la Turk" runs in 9/8 with a 2+2+2+3 subdivision, and Desmond's "Take Five" is in 5/4, a piece he wrote to give Morello a showcase in that meter. Columbia president Goddard Lieberson agreed to release the album only after the group recorded Gone with the Wind, a conventional album of Southern songs, as insurance. Issued in December 1959 with cover art by S. Neil Fujita, Time Out drew poor reviews at first but peaked at No. 2 on the Billboard album chart and became the first jazz album to sell a million copies; the Recording Industry Association of America certified it double platinum in 2011, and the Library of Congress added it to the National Recording Registry in 2005. Time Further Out (1961), Countdown: Time in Outer Space (1962), Time Changes (1964) and Time In (1966) continued the meter experiments, while Jazz Impressions of the U.S.A., of Eurasia, of Japan and of New York turned the quartet's travels into new pieces such as "Summer Song" and "Koto Song." With Iola, who wrote lyrics, he created the jazz musical The Real Ambassadors, recorded in September and December 1961 with Armstrong, the vocal group Lambert, Hendricks & Ross and Carmen McRae and performed at the 1962 Monterey Jazz Festival.

The classic quartet broke up in December 1967. Brubeck turned to large forms: the oratorio The Light in the Wilderness, premiered in Cincinnati in February 1968, and The Gates of Justice (1969), a cantata that sets the words of Martin Luther King Jr. beside Old Testament texts. He also led a trio with the bassist Jack Six and the drummer Alan Dawson and added Mulligan on baritone saxophone for Compadres (1968), Live at the Berlin Philharmonie (1970) and The Last Set at Newport (July 3, 1971). When Columbia declined to renew his contract in 1971 he moved to Atlantic. With his sons Darius, Chris and Dan he made Two Generations of Brubeck (1973), and in the fall of 1972 he, Mulligan and Desmond were reunited on the live We're All Together Again for the First Time. Desmond and Brubeck recorded the duo set 1975: The Duets, and the classic quartet regrouped for 25th-anniversary reunion concerts in 1976; Desmond's death from lung cancer on May 30, 1977, followed a tour with Brubeck. Brubeck then led a New Brubeck Quartet with his sons (Live at Montreux, July 17, 1977), began recording for Concord Jazz in 1979, and joined the Catholic Church in 1980 after completing his Mass To Hope. In the 1980s he led quartets with the clarinetist Bill Smith, Chris Brubeck and the drummer Randy Jones; they toured the Soviet Union in 1987, and Brubeck performed in Moscow at the 1988 Reagan-Gorbachev summit with Wright. From the early 1990s his quartet featured the saxophonist and flutist Bobby Militello with Jones and, in turn, the bassists Jack Six, Alec Dankworth and Michael Moore.

Brubeck received the National Medal of Arts and entered the DownBeat Hall of Fame in 1994, the Grammy Lifetime Achievement Award in 1996, a National Endowment for the Arts Jazz Masters award in 2000 and the Kennedy Center Honors in 2009, presented on his 89th birthday. In 2000 he and Iola founded the Brubeck Institute at the University of the Pacific. Brubeck passed away from heart failure on December 5, 2012, in Norwalk, Connecticut, one day before his 92nd birthday, on the way to a cardiology appointment with his son Darius; he is buried at Umpawaug Cemetery in Redding, Connecticut. On the day he died, Chick Corea and Gary Burton, on tour in Toronto, completed a tribute to him, with Corea playing "Strange Meadowlark" from Time Out. Iola Brubeck, his wife of seventy years, followed him on March 12, 2014. Four of their six children became professional musicians: the pianist Darius, the percussionist Dan, the multi-instrumentalist and composer Chris, and the cellist Matthew.

Brubeck set classical training against jazz improvisation. His mother's piano training and his study with Milhaud gave him a taste for counterpoint, fugue and polytonal harmony, and his best-known pieces layer contrasting rhythms, meters and tonalities, from the 9/8 of "Blue Rondo à la Turk" to the 7/4 of "Unsquare Dance." His approach covered a wide range, from refined lyricism to a forceful, bombastic attack. He is usually filed under cool jazz and, through Desmond's alto and the Bay Area base, the West Coast school, and his blend of classical forms with jazz was labeled third stream, though he was using it before the term existed. The Guardian's John Fordham judged his real achievement to be fusing European compositional ideas, demanding rhythmic structures, jazz song forms and improvisation in a way listeners could take in; the critic Robert Christgau called him a jazz hero for the rock and roll generation. Time Out itself drew negative reviews on release. His own tunes "In Your Own Sweet Way" and "The Duke" became standards, per his official biography. The Brubeck Institute's fellowship quintet has trained players such as the drummer Colin Stranahan, the vibraphonist Joel Ross and the saxophonist Chad Lefkowitz-Brown, and the pianist Glenn Zaleski counts Brubeck among the two pianists he learned the repertoire from, according to his profile.