Clifford Laconia Jordan was born on September 2, 1931, in Chicago, the only child of a middle-class family. He began on piano as a small child and took up the saxophone at 13. At DuSable High School, which had a celebrated music program, his schoolmates included the tenor saxophonists John Gilmore and Johnny Griffin. While still a student he played neighborhood parties and dances, and he went on to lead a dance band, work in rhythm-and-blues groups, and play bebop in Chicago with Max Roach and Sonny Stitt.

Jordan moved to New York in 1957 and began recording almost at once. That year he made three albums for Blue Note: Blowing In from Chicago, a two-tenor date with Gilmore recorded on March 3 with Horace Silver, bassist Curly Russell, and Art Blakey; Cliff Jordan, a septet session of June 2 with Lee Morgan, Curtis Fuller, alto saxophonist John Jenkins, pianist Ray Bryant, bassist Paul Chambers, and drummer Art Taylor; and Cliff Craft, recorded on November 10 with Art Farmer, pianist Sonny Clark, bassist George Tucker, and drummer Louis Hayes, and released in 1958. He also played on Blue Note sessions led by Chambers and Clark that year. Over the next several years he worked in the bands of Horace Silver (1957-58), J.J. Johnson (1959-60), Kenny Dorham (1961-62), and Max Roach, whose Impulse! albums Percussion Bitter Sweet (recorded in 1961) and It's Time (1962) both feature him.

In 1960 he began a working partnership with pianist Cedar Walton that lasted for the rest of his career; Walton is the pianist on Jordan's Riverside album Spellbound (1960), a quartet date with bassist Spanky DeBrest and drummer Albert Heath. Jordan's Jazzland albums followed: Starting Time (1961); A Story Tale (1961), shared with alto saxophonist Sonny Red and featuring Tommy Flanagan and Elvin Jones; and Bearcat, recorded in late 1961 and early 1962 with Walton, bassist Teddy Smith, and drummer J. C. Moses. In 1964 he joined the sextet of Charles Mingus, with Eric Dolphy, trumpeter Johnny Coles, pianist Jaki Byard, and drummer Dannie Richmond, and toured Europe with it. The sextet's 1964 concerts were recorded for live albums that include Town Hall Concert, Cornell 1964 (recorded March 18, 1964, and not issued until 2007), and the Enja releases Mingus in Europe. Dolphy died in West Berlin that June. Jordan's own These Are My Roots: Clifford Jordan Plays Leadbelly appeared on Atlantic in 1965, and he later toured West Africa and the Middle East with the pianist Randy Weston for the U.S. State Department.

In 1968 Jordan was music director of the first Dancemobile, a flatbed truck that took dance performances into New York neighborhoods, and in 1969 he moved briefly to Belgium, working there and frequently in Paris. He was back in New York by late 1969 and signed with Strata-East, the musician-run label, for which he made a trio of albums built largely on his own writing. In the World, recorded in 1969 with a cast that included Don Cherry, Kenny Dorham, trombonist Julian Priester, pianist Wynton Kelly, bassists Richard Davis and Wilbur Ware, and drummers Ed Blackwell, Roy Haynes, and Albert Heath, was issued in 1972. Glass Bead Games, a double album recorded in 1973 with pianists Stanley Cowell and Walton, bassists Bill Lee and Sam Jones, and drummer Billy Higgins, came out in 1974 and became his most celebrated record. The third, Drink Plenty Water, was recorded in 1974 with spoken word by the actor David Smyrl and a small vocal ensemble that included Jordan's daughter Donna, and it stayed unreleased until 2023. In 1972 he had played Lester Young in the Brooklyn Academy of Music production of Lady Day: A Musical Tragedy.

Through the 1970s and 1980s Jordan recorded steadily for Muse, SteepleChase, Bee Hive, Soul Note, Criss Cross, and other labels. He was a guest on Walton's A Night at Boomers albums (1973) and played in Walton's quartet in 1974-75. His own groups with Walton, Sam Jones, and Higgins appeared on SteepleChase as Clifford Jordan and the Magic Triangle (Firm Roots and The Highest Mountain, both recorded in West Germany in 1975, and three volumes of On Stage, recorded in the Netherlands the same year), and the same four players made the live Paris set Night of the Mark VII (Muse, 1975), named for his new Selmer tenor. In 1980 he was part of an all-star Independence Day celebration in Senegal with Dizzy Gillespie, Kenny Clarke, and Percy and Jimmy Heath. Hyde Park After Dark (1981) reunited him with Chicago veterans including tenor saxophonist Von Freeman, bass trumpeter Cy Touff, and pianist Norman Simmons. In the 1980s he renewed his partnership with Art Farmer on Mirage, You Make Me Smile, and several Contemporary albums, and made Two Tenor Winner with Junior Cook and Royal Ballads for Criss Cross. He was named a BMI Jazz Pioneer in 1984.

Jordan taught throughout his career, giving lessons through Jazzmobile, serving on the faculty of the Henry Street Settlement, and giving concerts in New York public schools. In the early 1990s he led a big band that played regularly at Eddie Condon's in New York. Its album Down Through the Years, recorded live there in 1991 and issued by Milestone in 1992, includes trumpeter Dizzy Reece, alto saxophonist Jerome Richardson, baritone saxophonist Charles Davis, euphonium player Bernard McKinney, who is credited there as Kiane Zawadi, and pianist Ronnie Mathews. Jordan passed away from lung cancer in New York on March 27, 1993, at the age of 61.

Jordan was a hard-bop tenor player with a robust, personal sound, rooted in the Chicago tenor tradition that he returned to on Hyde Park After Dark. A DownBeat reviewer heard a strong Sonny Rollins influence on Spellbound, and Scott Yanow wrote that he had a sound of his own almost from the start and that his playing became more distinctive during his time with Charles Mingus. He was a capable inside-and-outside player who held his own beside Eric Dolphy in the 1964 sextet, though Yanow noted that he was not a pacesetter in the avant-garde. The Strata-East records of the 1970s show his more ambitious side: Glass Bead Games sets hard-swinging rhythm sections to pieces named for Paul Robeson, John Coltrane, Cal Massey, and Eddie Harris, and Drink Plenty Water adds speech and voices. His compositions, among them "Highest Mountain," "Powerful Paul Robeson," and "Glass Bead Games," stayed in the repertoire of his regular partners, especially Cedar Walton. Late in life he carried the same language into the writing for his big band. Reviewers have tended to treat him as a dependable player rather than a trendsetter, and his reputation rests on steady, high-quality work as a leader and sideman from 1957 until his last years.