[5] Baker eloped from Missouri, where he began working as a university professor in 1955, to Chicago, Illinois, to marry Eugenia ("Jeanne") Marie Jones.

[7] Trained as a music educator and trombonist, Baker spent the early part of his career in the 1940s and 1950s as a jazz musician, performing and recording in the United States and in Europe.

A facial injury suffered in an automobile accident in 1953 ended his career as a trombonist, but Baker switched to cello and turned his attention to teaching and musical composition.

He was later named an IU distinguished professor and chair of the university's Jazz Studies department in the Jacobs School of Music.

He played in clubs along Indiana Avenue, the heart of the city's jazz scene of the late 1940s and early 1950s, with Jimmy Coe, Slide Hampton, J. J. Johnson, and Wes Montgomery.

He performed in clubs across the United States, including the Five Spot Café in New York City with George Russell in the late 1950s.

[8] Baker abandoned the trombone after a car accident in 1953 injured his jaw, but he began learning to play the cello in the early 1960s.

Because his facial injury in 1953 largely ended the performing aspect of his career, he returned to his home state of Indiana and began a period of increased interest in musical composition and pedagogy.

He is credited with writing more than 2,000 compositions, including his concerto "Levels" (1973) which received a Pulitzer Prize nomination, and the musical score for the PBS documentary film For Gold and Glory (2003), which won him an Emmy Award.

[1][16] Baker's best-known composition, which also received significant media attention, was Concertino for Cell Phones and Orchestra, a commission from Chicago Sinfonetta.

[2] He received over 500 commissions from individuals and ensembles, including compositions that he wrote for Gingold, Starker, Ruggiero Ricci, Harvey Phillips, trumpeter David Coleman, the New York Philharmonic, the Saint Paul Chamber Orchestra, the Beaux Arts Trio, the Fisk Jubilee Singers, and the Audubon Quartet, in addition to the Louisville Symphony, Ohio Chamber Orchestra, and the International Horn Society.

The Buselli–Wallarab Jazz Orchestra's album Basically Baker (2005) includes interpretations of his compositions, many of them written for big bands and ensembles.

[16] In 1991, in addition to his work at IU, Baker and Gunther Schuller became the artistic and musical directors of the Smithsonian Jazz Masterworks Orchestra, which was founded in 1990.

[20] Baker died on March 26, 2016, at the age of eighty-four in Bloomington from complications due to Parkinson's disease and Lewy body dementia.

"[21] With John Lewis With George Russell Baker wrote more than sixty books, including: He is also credited with authoring 400 articles.