Born in Cleveland, Ohio, United States, he learned to play the saxophone and started his first band, The Harlem Hotshots, while he was still in high school. In 1943, he was recruited as a saxophonist by bandleader Lucky Millinder, and the musicians in Millinder's band gave him the nickname "Bull Moose" for his appearance. He began singing when required to stand in for Wynonie Harris at a show in Texas.
Millinder encouraged Jackson to sign a solo contract with Syd Nathan of King Records to play rhythm and blues. He first recorded in his own right in 1946, with "I Know Who Threw the Whiskey", an answer song to Millinder's "Who Threw the Whiskey in the Well". The following year, his recording of "I Love You, Yes I Do" reputedly became the first R&B single to sell a million copies, holding the #1 spot on the R&B chart for three weeks and crossing over to the pop chart, where it made #24.
He formed his own group, The Buffalo Bearcats, and over the next five years recorded in a wide variety of musical styles, including both romantic crooning and bawdy jump blues. Other big hits in 1948 included the double-sided hit "All My Love Belongs to You" / "I Want a Bowlegged Woman", and his biggest R&B chart hit, "I Can't Go On Without You", which stayed at # 1 on the R&B chart for eight weeks. He also made an appearance in the 1948 film, Boarding House Blues, with Millinder.
In 1949, he covered "Why Don't You Haul Off and Love Me" a song that been successful for Wayne Raney as well as several country and western performers.
Jackson toured throughout the late 1940s and early 1950s. Around 1951, his band included bebop composer and arranger Tadd Dameron on piano, and another jazz musician, Benny Golson, on saxophone.
Some of Jackson's later risqué material, including "Big Ten Inch Record" (later covered by Aerosmith on Toys in the Attic) and "Nosey Joe" (written by Leiber and Stoller), both from 1952, were too suggestive for airplay, but remained popular.
Jackson continued to record until the mid-1950s, but as musical tastes changed began working for a catering firm in Washington, D.C. In 1961 he re-recorded and had a minor hit with "I Love You, Yes I Do".
In the early 1980s he was persuaded by Carl Grefenstette to perform and record again with the Pittsburgh R&B revival band, The Flashcats, who had been playing his songs, and to record the album Moosemania! in 1985. Jackson also toured nationally and internationally. However, his health began to fail, and he died of lung cancer in Cleveland in 1989. blues rhythm and blues jump blues bebop jazz