Sonny Stitt was born Edward Hammond Boatner Jr. on February 2, 1924, in Boston, Massachusetts. His father, Edward Boatner, was a baritone, composer, and college music professor; his mother taught piano, his brother trained as a classical pianist, and his sister sang on Broadway. He was placed for adoption in 1924 and raised by the Stitt family in Saginaw, Michigan, where he took the surname Stitt and later the first name Sonny. He studied piano from the age of seven until his parents bought him a clarinet, and in high school he played in the Len Francke Band, a local swing outfit. By fifteen he was modeling his alto playing on Johnny Hodges and Benny Carter, but hearing Charlie Parker on a Jay McShann record turned him into a bebop player.

In 1943, while touring with Tiny Bradshaw's band, Stitt tracked Parker down in Kansas City, and the two jammed on blues at the Gypsy Tea Room. Parker told him he sounded too much like him, and Stitt's answer, that it was the only way he knew to play, became the usual shorthand for a comparison that followed him for years. In the 1940s he worked in Bradshaw's big band, then in Billy Eckstine's orchestra alongside Gene Ammons and Dexter Gordon, and in Dizzy Gillespie's big band; his first recordings date from 1945 with Gillespie's groups. He led the Bebop Boys in 1946 and a group called Galaxy in 1948. By the end of the decade he was playing tenor saxophone as well as alto, and on tenor he sounded less like Parker. In 1949 and 1950 he recorded for Prestige with Bud Powell and J.J. Johnson, and in 1950 he co-led sessions with Ammons that renewed their partnership.

The 1950s were his most productive years on record. For Roost he made a 1953 date of arrangements by Johnny Richards, the live Jazz at the Hi-Hat (1954), a two-tenor encounter with Eddie "Lockjaw" Davis recorded at Birdland in 1954, and in 1955 a set of arrangements by Quincy Jones. At Verve he recorded For Musicians Only on October 16, 1956, in Los Angeles with Gillespie and Stan Getz, and Sonny Side Up in December 1957, pairing him on tenor with Sonny Rollins and Gillespie. He also played the 1957 Newport Jazz Festival, where a July 7 set with Oscar Peterson, Roy Eldridge, and Jo Jones was recorded, and made Sonny Stitt Sits In with the Oscar Peterson Trio in 1959. Late in the decade he tried Afro-Cuban material for Roost and Verve, and he made albums for Argo in Chicago. After giving up heroin in the late 1950s he drank heavily, and alcoholism later cut into his productivity.

In 1960 he joined Miles Davis's quintet for a European tour with Wynton Kelly, Paul Chambers, and Jimmy Cobb; concerts from Paris and Stockholm have been issued, and Davis let him go because of his drinking. The early 1960s produced the records for which many tenor fans know him best: Boss Tenors (recorded August 1961) and Boss Tenors in Orbit! (1962) with Ammons, whose own legal troubles interrupted their sessions, and Soul Summit (1962) with Ammons and organist Jack McDuff. For Prestige he recorded a run of organ-combo albums, many with Don Patterson, including Shangri-La and Soul People (with Booker Ervin), both from 1964. He recorded Stitt Plays Bird for Atlantic in 1963 with Jim Hall on guitar, two albums for Impulse!, Now! (1963) and Salt and Pepper (with Paul Gonsalves, 1963), and Inter-Action (1965) with Zoot Sims. He played at Ronnie Scott's Club in London in 1964 and again in 1966, and in 1966 and 1967 he was one of the first jazz players to record with Selmer's Varitone amplification system, on What's New!!! and Parallel-a-Stitt.

His recording pace eased in the 1970s, but his playing recovered. In 1971 he made four albums, among them Turn It On! with organist Leon Spencer, guitarist Melvin Sparks, and drummer Idris Muhammad, and in 1972 he cut Tune-Up! and Constellation with Barry Harris and Sam Jones, sessions that critics rank among his best. He joined the Giants of Jazz, whose 1971 world tour and live album also featured Gillespie, Thelonious Monk, Art Blakey, Kai Winding, and Al McKibbon, and he reunited with Ammons for several albums until Ammons passed away in 1974. A series of alcohol-induced seizures finally led him to quit drinking for good. In the late 1970s he toured with Red Holloway, and six weeks before his death he recorded two consecutive sessions with George Duvivier, Jimmy Cobb, Bill Hardman, and either Junior Mance or Walter Davis Jr. on piano. He was diagnosed with cancer in 1982 and passed away in Washington, D.C., on July 22, 1982, at the age of 58. He is buried in a wall crypt at Fort Lincoln Cemetery in Brentwood, Maryland.

Stitt played with a warm tone, fast fingers, and a command of bebop vocabulary that let him run chord changes at any tempo, and he was equally at home with blues and ballads. The critic Dan Morgenstern nicknamed him the Lone Wolf because he rarely kept the same sidemen for long despite constant touring. For years he was called a Parker imitator, and the drummer Kenny Clarke answered that even without Parker there would have been a Sonny Stitt. His tenor playing did most to settle the question: reviewers described it as bop-oriented against the more soulful sound of Gene Ammons, and on alto he kept paying tribute to Parker for the rest of his life, from Stitt Plays Bird (1963) to I Remember Bird (1976). His early alto models were Johnny Hodges and Benny Carter, and he drew on Lester Young as well as Parker, writing blues tributes such as "Blues for Prez and Bird." The Ammons partnership is counted among the great two-tenor pairings, alongside Zoot Sims with Al Cohn and Johnny Griffin with Lockjaw Davis. From the early 1960s he was a regular guest on organ-combo dates, where his bop lines met the blues groove of Jack McDuff and Don Patterson, and in the late 1960s the Varitone gave his sound an electronic edge that some critics disliked and that he eventually set aside. Scott Yanow regards Tune-Up! (1972) as his definitive album, and Down Beat gave it five stars.