Weldon Leo "Jack" Teagarden was born on August 20, 1905, in Vernon, Texas, the oldest of four children, all of whom became musicians: his brother Charlie played trumpet, his sister Norma piano, and his brother Clois, known as Cub, drums. His father, Charles, worked in the oil fields and played cornet part-time; his mother, Helen, was a pianist who accompanied silent films, and as a boy Jack played trombone-and-piano duets with her in a Vernon movie theater. After his father's death in 1918 the family moved to Chappell, Nebraska, where mother and son again worked in the local theater, and the next year to Oklahoma City. Teagarden was largely self-taught, and he developed an unusual set of alternate slide positions and special effects on the instrument.

He turned professional at sixteen in San Antonio with Cotton Bailey's dance and jazz band, and in the same year joined Peck Kelley's group in Houston, where Paul Whiteman heard the band and offered Teagarden a place in his New York orchestra. Teagarden spent several more years on the road with Texas and regional bands, made a first trip to New York in 1926 with Doc Ross's Jazz Bandits, and returned on his own in 1927. After a stint with the Tommy Gott orchestra he landed a chair with Ben Pollack's band, where he won the first-trombone spot over Glenn Miller and made more than 300 recordings. His first record date, in 1927, was with the Kentucky Grasshoppers, a Pollack offshoot.

Through the late 1920s and early 1930s he freelanced widely in New York and recorded with Louis Armstrong, Benny Goodman, Bix Beiderbecke, Red Nichols, Eddie Condon, Jimmy McPartland, Mezz Mezzrow and Fats Waller. A 1929 session organized by Condon that produced "Knockin' a Jug," with Armstrong, is counted among the first integrated jazz recording dates. On September 15, 1930, he was on Hoagy Carmichael's Victor session of "Georgia on My Mind" with Beiderbecke, Eddie Lang, Joe Venuti, Jimmy Dorsey and Bud Freeman, and on November 24, 1933, he was in the pickup band behind Bessie Smith on her last recording session. He also began singing on records, in a relaxed, blues-inflected style, and he and Miller are credited with adding the verse to "Basin Street Blues" that most singers now use; it became one of his most frequently played numbers.

Seeking financial security in the Depression, Teagarden signed an exclusive contract with the Paul Whiteman orchestra and stayed from 1933 to 1938, leaving when the band's limited jazz repertoire wore thin. In 1939 he formed his own big band, which was admired by musicians but lost money and was disbanded in 1947. In 1943 the sixteen-year-old Stan Getz joined the band, and Teagarden became his guardian. He also led small groups, including his Big Eight, won the 1944 Esquire Gold Award, and appeared in the film Birth of the Blues (1941).

In 1947, after a May concert at New York's Town Hall, Louis Armstrong reorganized around a small group, the All Stars, and Teagarden became its trombonist and a featured vocalist, a partnership documented on "Rockin' Chair" and on the Symphony Hall (Boston, November 30, 1947) and Pasadena (January 30, 1951) concert albums. He left in late 1951 to lead his own small group, the Jack Teagarden All Stars, which recorded for Capitol in 1956 to 1958, Roulette from 1959 to 1961 and Verve in 1961 and 1962. He was a featured performer at the 1957 Newport Jazz Festival, toured Europe and Asia in 1957 to 1959 on a government-sponsored goodwill tour, and, with Armstrong's All Stars, appears in the film Jazz on a Summer's Day (1959), shot at the 1958 Newport festival. He also redesigned trombone mouthpieces, mutes and water valves.

Teagarden was found dead in his room in New Orleans on January 15, 1964, hours before he was due to perform; he was 58, and the cause of death was attributed to bronchial pneumonia. He was buried at Forest Lawn Memorial Park in the Hollywood Hills. He was inducted into the Down Beat Jazz Hall of Fame in 1969 and the Big Band and Jazz Hall of Fame in 1985, and his honors also include the ASCAP Jazz Wall of Fame and the Texas Music Hall of Fame.

Teagarden, who had relatively short arms, did not rely on the broad glissandos of the traditional tailgate trombone. He built a style on embouchure control, trumpet-like phrasing, upper-register solos, lip trills and a loose relationship to a strict solo beat, with a warm, vocal tone. He grew up in a part of Texas with a large Black population and absorbed blues and gospel early, and he is counted among the first jazz musicians to work blue notes into his playing; his singing carried the same blues core. Clarinetist Pee Wee Russell rated him the best trombonist in the world, and the critic Gunther Schuller praised his effortless technical command and his lack of exhibitionism. Tommy Dorsey is reported to have changed his own approach to avoid comparison with him, and Glenn Miller is said to have played down his own trombone playing after working beside him in Pollack's band. Wycliffe Gordon names him, with J.J. Johnson and Louis Armstrong, among his principal influences. His work is best placed in the Dixieland and swing traditions, with a blues depth that set him apart from both.