Edward Hammond Boatner, Jr. was born in
 and grew up in
Saginaw, Michigan. He had a musical background: his father,
Edward Boatner, was a baritone singer, composer and college music professor; his brother was a classically trained pianist; and his mother was a piano teacher.
Sonny was given up for adoption in 1924 by his father. No one seems to know why Boatner gave his son away, but the child was adopted by the Stitt family, who raised him in Saginaw.
 He later began calling himself "Sonny". While in high school in Saginaw, Stitt played in the Len Francke Band, a local popular swing band.
In 1943, Stitt first met
Charlie Parker, and as he often later recalled, the two men found that their styles had an extraordinary similarity that was partly coincidental and not merely due to Stitt's emulation. Parker is alleged to have remarked, "Well, I'll be damned, you sound just like me", to which Stitt responded: "Well, I can't help the way I sound. It's the only way I know how to play."
Kenny Clarke remarked of Stitt's approach: "Even if there had not been a Bird, there would have been a Sonny Stitt".
Stitt had played in some
swing bands in the early 1940s and was featured in
Tiny Bradshaw's big band in the early forties. He replaced Charlie Parker in
bop big band in 1945 and in 1946 made the first recordings under his own name for Savoy Records, which established his bop credentials.
Stitt played alto saxophone in
big band alongside future bop pioneers
Dexter Gordon and
Gene Ammons beginning in 1945 when he started to play tenor saxophone more frequently, in order to avoid being referred to as a Charlie Parker imitator. Later on, he played with Gene Ammons and
Bud Powell. Stitt spent time at the Federal prison in
Lexington, Kentucky, between 1948 and 1949 for selling narcotics.
Stitt, when playing tenor saxophone, seemed to break free from some of the criticism that he was imitating Parker's style, and he began to develop a far more distinctive sound on tenor.
 He played with other bop musicians
Bud Powell and
Eddie "Lockjaw" Davis, a fellow tenor with a distinctly tough tone in comparison to Stitt, in the 1950s and recorded a number of sides for
Prestige Records label as well as albums for
Roost. Stitt experimented with
Afro-Cuban jazz in the late 1950s, and the results can be heard on his recordings for Roost and Verve, on which he teamed up with
Thad Jones and
Chick Corea for Latin versions of such standards as "
Miles Davis briefly in 1960, and recordings with Davis' quintet can be found only in live settings on the tour of 1960. Concerts in Manchester and Paris are available commercially and also a number of concerts (which include sets by the earlier quintet with
John Coltrane) on the record Live at Stockholm (
Dragon), all of which featured
Jimmy Cobb and
Paul Chambers. However, Miles fired Stitt due to the excessive drinking habit he had developed, and replaced him with
Hank Mobley. Later in the 1960s, Stitt paid homage to Parker on the album Stitt Plays Bird, which features
Jim Hall on guitar.
Stitt recorded a number of memorable records with his friend and fellow saxophonist
Gene Ammons, interrupted by Ammons' own imprisonment for narcotics possession. The records recorded by these two saxophonists are regarded by many as some of both Ammons and Stitt's best work, thus the Ammons/Stitt partnership went down in posterity as one of the best duelling partnerships in jazz, alongside
Zoot Sims and
Al Cohn, and
Johnny Griffin with
Eddie "Lockjaw" Davis. Stitt would venture into
soul jazz, and he recorded with fellow tenor saxophonist
Booker Ervin in 1964 on the Soul People album. Stitt also recorded with
Duke Ellington alumnus
Paul Gonsalves in 1963 for
Impulse! on the
Salt And Pepper album in 1963. Around that time he also appeared regularly at
Ronnie Scott's in London, a live 1964 encounter with
Ronnie Scott, The Night Has A Thousand Eyes, eventually surfaced, and another in 1966 with resident guitarist
Ernest Ranglin and British tenor saxophonist
Dick Morrissey. Stitt was one of the first jazz musicians to experiment with the Selmer
Varitone amplification system as heard on the albums What's New in 1966 and Parallel-A-Stitt in 1967.