Jean-Baptiste Illinois Jacquet was born on October 30, 1922, in Broussard, Louisiana, to Gilbert Jacquet and Marguerite Trahan, both Creoles of color. The family moved to Houston, Texas, while he was an infant, and he grew up there as one of six children. His father led a band part-time, and as a boy Jacquet played in it, mostly on alto saxophone; his older brother Russell played trumpet and his brother Linton drums. At 15 he joined the Milton Larkin Orchestra, a Houston-area dance band, while attending Wheatley High School.

In 1939 he moved to Los Angeles, where he met Nat King Cole and sat in now and then with Cole's trio. In 1940 Cole introduced him to Lionel Hampton, who was putting together a big band after returning to California. Hampton wanted to hire him but asked him to switch to tenor saxophone. On May 26, 1942, the Hampton orchestra recorded "Flying Home" for Decca, with the 19-year-old Jacquet taking a long tenor solo built to weave in and out of the arrangement. The record was a hit, the solo became the climax of the band's live shows, and it is widely cited as the first rhythm and blues saxophone solo. The tenor players who followed him in the band, among them Arnett Cobb and Dexter Gordon, played it almost note for note, and Jacquet grew tired of having to bring down the house with it every night. He left Hampton in 1943 for Cab Calloway's orchestra and appeared with Calloway's band in the film Stormy Weather (1943).

In 1944 he returned to California and started a small band with his brother Russell and a young Charles Mingus. That year he appeared in the Academy Award-nominated short film Jammin' the Blues alongside Lester Young, and he was on the bill of the first Jazz at the Philharmonic concert, held July 2, 1944, at the Philharmonic Auditorium in Los Angeles, where he, Cole and guitarist Les Paul created the evening's biggest sensation. In 1946 he moved to New York and joined the Count Basie Orchestra, replacing Young. His own sessions of 1945 to 1950 for Philo and Aladdin, Apollo, ARA, Savoy and RCA Victor were collected in a four-disc Mosaic set in 1996. In 1949 he wrote the instrumental "Black Velvet" with the arranger Jimmy Mundy; Al Stillman added lyrics, and Harry James recorded it that year as "Don'cha Go 'Way Mad," a song later performed by Frank Sinatra and Ella Fitzgerald among many others. J.J. Johnson worked in his band from 1947 to 1949, and baritone saxophonist Cecil Payne from 1952 to 1954, according to their own profiles.

Jacquet was a featured soloist on Jazz at the Philharmonic tours in the late 1940s and returned to them in 1955, and he recorded for Norman Granz's Clef and Verve labels in the 1950s, including a 1954 meeting with Ben Webster. He also used his standing against segregation. In Houston he had earlier made the Rice Hotel drop its rule that Black guests use an alley entrance by threatening to cancel his band's engagement. On October 5, 1955, Granz brought a Jazz at the Philharmonic package with Jacquet, Fitzgerald, Dizzy Gillespie, Oscar Peterson and Buddy Rich to Houston's Music Hall for a desegregated concert, with no advance ticket sales and the "white" and "black" signs removed. Houston vice officers then used a dice game in a dressing room as the pretext to arrest Jacquet, Gillespie, Fitzgerald and her assistant, who were taken to the station for the waiting photographers, paid their fines, and returned to play the second set.

In the 1960s and 1970s he worked mostly in small groups and often in Europe. For Argo he made The Message and Desert Winds with guitarist Kenny Burrell in 1963 and 1964, and he played on the singer Johnny Hartman's I Just Dropped by to Say Hello, recorded in October 1963. At Prestige in 1968 and 1969 he made Bottoms Up, The King!, The Soul Explosion and The Blues; That's Me! for producer Don Schlitten, and in the 1970s he recorded for Black Lion and Black & Blue with organists Wild Bill Davis and Milt Buckner and drummer Jo Jones. From 1981 until his death he led the Illinois Jacquet Big Band, which was recorded live at the Village Vanguard in 1986 and 1987 and at the Blue Note in 1987, and which made Jacquet's Got It! for Atlantic in 1988. In 1983 he became the first jazz musician to serve as an artist-in-residence at Harvard University, and in 1993 he played "C-Jam Blues" with President Bill Clinton at an inaugural event. The documentary Texas Tenor: The Illinois Jacquet Story is about his life.

His last performance was on July 16, 2004, at Lincoln Center in New York. He passed away six days later, on July 22, 2004, at the Queens home he shared with his partner Carol Scherick; he was 81, and the cause was a heart attack. A memorial service was held at Riverside Church, and he is buried at Woodlawn Cemetery in the Bronx. In 2008 the Chapel of the Sisters at York College in Jamaica, Queens, was restored and rededicated as the Illinois Jacquet Performance Space, and the Illinois Jacquet Foundation supports scholarships and education in his name.

Jacquet was a leading figure in the Texas tenor tradition, alongside Buddy Tate and James Clay, and a pioneer of the honking tenor sound: a big, shouting tone that stressed the instrument's lowest and highest registers and took the brash sound that had come from Lester Young's playing further. Behind the raw surface he was a melodic improviser at fast tempos and on ballads, and he was one of the few jazz musicians to double on bassoon, which he played on dates such as The Message (1963) and The King! (1968). His solos of the 1940s and his Jazz at the Philharmonic showpieces shaped the tenor saxophone style of rhythm and blues and early rock and roll. Coleman Hawkins's profile traces a line from Hawkins and Ben Webster through Herschel Evans, Buddy Tate and Don Byas to Jacquet, Paul Gonsalves and Arnett Cobb. Cobb, who also played "Flying Home" with Lionel Hampton, Eddie "Lockjaw" Davis, Jimmy Forrest and Sonny Rollins are the players whose work Wikipedia says carries his influence. Stanley Turrentine and Houston Person have each named him as an influence, and the blues guitarist B.B. King cited his phrasing as a model, according to their profiles. His compositions include "Black Velvet," known as "Don'cha Go 'Way Mad," and "Robbins' Nest," written with the pianist Sir Charles Thompson.