Truman Elliot "Jack" Jenney was born on May 12, 1910 in Mason City, Iowa. The Jenney family moved to Dubuque, Iowa after his father became a music instructor at Columbia College (now Loras College) in 1913. Jack Jenney studied trumpet with his father at the age of 8, but eventually switched to the trombone, the instrument that he would become a master of. He became so skilled with the trombone he even toured with his father's national touring band, The Grandioso Band. In 1922 he also performed with a Dubuque jazz band, Art Braun & His Novelty Boys. He entered Dubuque Senior High school, but had to leave when his family moved to Cedar Rapids, Iowa. He won a music scholarship to Culver Military Academy in Indiana, where he graduated.

He began playing with Austin Wylie's band in 1928. By 1932 he had moved to New York City and played with Isham Jones & His Orchestra. He worked with numerous radio orchestras, including those directed by Victor Young, Freddie Rich, and Lennie Hayton. At one time he maintained a schedule of playing with 10 to 20 major radio programs a week, plus recording and touring. He also played for Bing Crosby, Mal Hallett, Chick Bullock, Glenn Miller, Smith Ballew, Jack Shilkret, Benny Goodman, Red Norvo's Jazz Septet, and Jimmy Dorsey & His Orchestra. He married popular vocalist Kay Thompson (his second wife, whom he later divorced) and conducted recording sessions for her in 1937. He later married singer Bonnie Lake.

He started recording songs under his own name in 1938, and in 1939 formed a touring band (which eventually went bankrupt). He then joined Artie Shaw & His Orchestra, where his famous trombone solo on the October 7, 1940 recording of Stardust is considered by many to be a classic moment in the history of big band swing and jazz. He appeared in the jam session at the end of the 1942 movie Syncopation and in the 1943 movie Stage Door Canteen.

He served in the U. S. Navy for a short time in 1943 and 1944, where he led a band, before being discharged for health reasons. He continued to perform on the West Coast before he died of complications following an emergency appendectomy in Los Angeles, California on December 16, 1945. Shortly before his death he co-wrote Man With A Horn (also known as The Man With The Horn) with his wife Bonnie Lake and Eddie DeLange. He also co-wrote City Night with Alec Wilder, and What More Can I Give You? with Kay Thompson.