Dexter Keith Gordon was born on February 27, 1923, in Los Angeles. His father, Dr. Frank Gordon, was one of the first African American physicians practicing in the city, a Howard University Medical School graduate who arrived in 1918 and counted Duke Ellington and Lionel Hampton among his patients. His mother, Gwendolyn Baker, was the daughter of Captain Edward Lee Baker Jr., one of five African American Medal of Honor recipients of the Spanish American War. Gordon took up the clarinet at thirteen, moved to alto saxophone at fifteen and settled on tenor at seventeen, studying with the multi-instrumentalist Lloyd Reese while at Thomas Jefferson High School and playing in school bands alongside Chico Hamilton and Buddy Collette. He stood six feet six inches, which earned him the nickname "Long Tall Dexter" before he had made a record under his own name.

He joined Lionel Hampton's band in December 1940 and stayed roughly three years, sitting in a saxophone section with Illinois Jacquet and Marshal Royal that left him almost no solo space. He was drafted into the Army in 1942 and assigned to the Signal Corps. In 1943 he stretched out on a small-label session under Nat King Cole with trumpeter Harry "Sweets" Edison, and during 1944 he passed through the Fletcher Henderson and Louis Armstrong big bands before landing in Billy Eckstine's orchestra, where he traded choruses with Gene Ammons on "Blowin' the Blues Away." The 1942 to 1944 recording ban kept most of that work off commercial discs; what survives of it survives on V-Discs cut for overseas troops. By late 1944 Gordon was living in New York and playing the bebop jam sessions, recording with Dizzy Gillespie on "Blue 'n' Boogie" and "Groovin' High" in early 1945 and cutting his first leader dates for Savoy later that year.

Back in Los Angeles from the summer of 1946, he became a fixture of the Central Avenue scene and led sessions for Ross Russell's Dial label in 1947. The tenor duels he fought there with Wardell Gray, documented between 1947 and 1952 on "The Chase," "The Hunt," "Move" and "The Steeplechase," were a popular concert draw, and "The Hunt" picked up a second life when Jack Kerouac named it in On the Road. Younger Los Angeles players who shared bandstands with him in these years included Hampton Hawes, Joanne Brackeen, Walter Norris and Don Friedman. Then heroin took the decade away from him. He was incarcerated at Chino from 1953 to 1955, made Daddy Plays the Horn and Dexter Blows Hot and Cool on his release with Leroy Vinnegar on bass and Carl Perkins at the piano on the latter, and was in and out of custody until a final release from Folsom in 1959. He worked his way back through the Los Angeles stage production of Jack Gelber's play The Connection in 1960, taking over the saxophone chair from Jackie McLean and contributing two tunes of his own, "Ernie's Tune" and "I Want More," to the score.

Gordon signed with Blue Note in 1961 and produced, in four years, the run of records his reputation still rests on. Doin' Allright and Dexter Calling... came from three days of sessions in May 1961 with Freddie Hubbard, Horace Parlan, Kenny Drew, Paul Chambers, George Tucker, Al Harewood and Philly Joe Jones. Go! and A Swingin' Affair followed in August 1962 with the label's house rhythm section of Sonny Clark, Butch Warren and Billy Higgins; Gordon named Go! his own favorite, and in the class announced in March 2019 the Library of Congress added it to the National Recording Registry. Our Man in Paris (1963) put him in a Paris studio with Bud Powell, Kenny Clarke and the French bassist Pierre Michelot. One Flight Up (1964) added Donald Byrd and the young Danish bassist Niels-Henning Ørsted Pedersen. Gettin' Around (1965) and the shelved Clubhouse, unreleased until 1979, brought in Bobby Hutcherson and Barry Harris.

He left the United States soon after recording A Swingin' Affair and stayed away for fourteen years, living mainly in Copenhagen and Paris. Europe suited him: he said plainly that he met less racism there and found jazz musicians better respected. The Jazzhus Montmartre in Copenhagen became his home room, and SteepleChase would eventually issue dozens of tapes from those nights, including the 1966 date with the South African drummer Makaya Ntshoko released as Stella by Starlight. His standing partnership with pianist Kenny Drew ran through most of the period. He moved to Prestige from 1965 to 1973, recording The Tower of Power! and More Power! with James Moody, Barry Harris and Buster Williams; The Panther! with Tommy Flanagan, Larry Ridley and Alan Dawson; The Jumpin' Blues with Wynton Kelly, Sam Jones and Roy Brooks; and a Chicago reunion with Gene Ammons issued as The Chase! He signed an exclusive contract with the Danish label SteepleChase in 1975, which produced The Apartment, Stable Mable, the three Swiss Nights volumes and Biting the Apple, the last of them cut in New York with Barry Harris, Sam Jones and Al Foster.

Gordon came home for good in 1976. A run at the Village Vanguard that autumn with Woody Shaw, Ronnie Mathews, Stafford James and Louis Hayes was recorded and released by Columbia as Homecoming, and the reception was extraordinary. "There was so much love and elation," he said of it. "After the last set they'd turn on the lights and nobody would move." Columbia followed with the eleven-piece Sophisticated Giant in 1977, arranged by Slide Hampton with Frank Wess, Bobby Hutcherson, Victor Lewis and Woody Shaw, and with Manhattan Symphonie and Great Encounters, while Blue Note issued three volumes taped at the Keystone Korner in San Francisco with George Cables, Rufus Reid and Eddie Gladden. He was DownBeat's Musician of the Year in 1978 and 1980 and entered the magazine's Hall of Fame in 1980. In 1986 the National Endowment for the Arts named him an NEA Jazz Master and the French Ministry of Culture made him an Officier des Arts et Lettres.

His last major work was on screen. In 1986 he played Dale Turner, an expatriate saxophonist in 1950s Paris drawn loosely from Lester Young and Bud Powell, in Bertrand Tavernier's Round Midnight, and became the first jazz musician nominated for the Academy Award for Best Actor. The companion album The Other Side of Round Midnight, with Herbie Hancock, Freddie Hubbard, Ron Carter, Cedar Walton and Tony Williams, won him a Grammy Award and was the last record issued under his name. He took a non-speaking part in Awakenings, released after his death, and appeared as a sideman on Tony Bennett's 1987 album Berlin. A lifelong smoker weakened through the 1980s by emphysema, Gordon passed away in Philadelphia on April 25, 1990, of kidney failure and cancer of the larynx, at sixty-seven. His widow Maxine Gordon completed the biography Sophisticated Giant: The Life and Legacy of Dexter Gordon for the University of California Press in 2018.

Gordon played big. His tone was wide and unhurried, he sat conspicuously behind the beat, and he built solos out of long horizontal lines rather than the vertical scramble much of bebop favored, which is what let a bop player of his generation keep sounding contemporary into the 1970s. Lester Young was the root influence, with Herschel Evans and Illinois Jacquet audible underneath; his habit of dropping quotations into a solo, anything from "Happy Birthday" to a Wagner melody, was frequent enough to count as a signature rather than a joke. He was in turn one of the first tenor players John Coltrane and Sonny Rollins took from, and the influence then ran back the other way, audibly so in the harder, more modal playing of his Blue Note records. Onstage he was warm and funny and made a point of reciting a ballad's lyric into the microphone before playing it. His reach into later generations of tenor players is direct and documented: Craig Handy has described hearing Gordon play "Body and Soul" on the radio at eleven as the thing that decided him on the saxophone, Chad Lefkowitz-Brown names Go! as the record that turned him toward jazz, and Mark Turner counts him in the small group of tenor players he listened deepest to.