Irving Sidney Jordan was born on April 1, 1922, in Brooklyn, New York, and grew up there, attending Boys High School. He started piano lessons as a child and turned professional in 1941, when his first major engagement was in the band of Coleman Hawkins. By 1946 he had also worked with the Savoy Sultans and with the big band of Roy Eldridge.

In 1947 he became the regular pianist in Charlie Parker's quintet, a post he held through 1948 alongside Miles Davis, Max Roach and the bassist Tommy Potter. The group played the clubs on 52nd Street, including the Three Deuces, where the photographer William P. Gottlieb caught the band in August 1947. At the Dial sessions of late 1947 Jordan, then 25, played on "Dewey Square," "Bongo Bop," "Bird of Paradise" and "Embraceable You." His piano introduction to "Embraceable You" is the passage listeners tend to cite first when his name comes up.

After leaving Parker he worked in the quintet that Sonny Stitt and Gene Ammons co-led in 1950 and 1951, and with Stan Getz in 1949 and again in 1952 and 1953. He made his first records as a leader in January 1954, a trio date with the bassist Gene Ramey and the drummer Lee Abrams, released in France on the Swing label. His best-known composition, "Jordu," dates from 1953; Clifford Brown and Max Roach recorded it on August 3, 1954, and it became a standard through their version. In October and November 1955 he cut the sessions issued as Duke Jordan Trio and Quintet for Don Schlitten's Signal label, with Percy Heath and Art Blakey in the rhythm section and, on some tracks, Cecil Payne and the trombonist Eddie Bert.

In 1959 he worked in Paris on the music for Roger Vadim's film Les Liaisons Dangereuses, co-composing under the name Jacques Marray with contributions from Thelonious Monk; the soundtrack was recorded by Art Blakey's Jazz Messengers with the tenor saxophonist Barney Wilen, with Jordan himself at the piano on one track, and Jordan also led a quintet in recordings of his own music for the film, issued in 1962. One of his pieces for it, "No Problem," went on to be recorded many times. His best-regarded leader album from these years is Flight to Jordan, cut for Blue Note at Rudy Van Gelder's studio on August 4, 1960, with the trumpeter Dizzy Reece, the tenor saxophonist Stanley Turrentine, the bassist Reggie Workman and the drummer Art Taylor. Work then thinned out, and for a period in the mid-1960s he drove a taxi in New York.

In 1973 he began recording for the Danish SteepleChase label, starting with trio albums made with the bassist Mads Vinding and the drummer Ed Thigpen, including Flight to Denmark and Two Loves. In 1978 he moved to Copenhagen, where he lived for the rest of his life, and over the following years he recorded an extensive run of SteepleChase albums: trios with Sam Jones and Al Foster, with the bassist Wilbur Little and Roy Haynes, with Philly Joe Jones, and with Niels-Henning Ørsted Pedersen and Billy Hart, plus the quartet date Duke's Artistry with Art Farmer. He also accompanied Chet Baker on No Problem (recorded 1979) and played with Art Pepper in Copenhagen in 1981. Japanese labels recorded him through the late 1980s and early 1990s, and his last albums date from the mid-1990s.

From 1952 to 1962 he was married to the singer Sheila Jordan; their daughter is Tracey J. Jordan. He passed away on August 8, 2006, in Valby, a district of Copenhagen, at the age of 84.

Jordan is remembered as a pianist of restraint. The critic Doug Ramsey credited him with a gentle touch, subtle harmony and a gift for melodic invention, and described his ballad introductions as small masterpieces; with Charlie Parker he often had about sixteen bars to solo and shaped each one as a short story with a beginning, middle and end. An AllMusic reviewer called him perhaps the most subdued of the first-generation bebop pianists, favoring simply built chords and medium tempos, and some listeners hold that his style hardly changed over a career of more than five decades. He is said to have drawn on Art Tatum and Teddy Wilson, and he came of age in the Harlem clubs where Bud Powell and Thelonious Monk were helping to define the new music. Two of his compositions have outlived most of his recordings: "Jordu," taken up by Clifford Brown, Stan Getz, Chet Baker and Charlie Byrd among others (and given a lyric titled "Life Is a Groove" by Karrin Allyson), and "No Problem," recorded by Art Blakey as "No Hay Problema" and by Chet Baker.