Morgan was a jazz prodigy, joining the Dizzy Gillespie big band at 18, remaining a member for two years. Beginning in 1956, he began recording as a leader, mainly for the Blue Note label, eventually he recorded twenty-five albums for the company. Morgan's principal influence as a player was Clifford Brown, having had direct contact with him before Brown's premature death.
He was also a featured sideman on several early Hank Mobley records, and John Coltrane's Blue Train. On the latter LP, he even played a bent-up horn like Gillespie's. Joining Art Blakey's Jazz Messengers in 1958 further developed his talent as a soloist and writer. He toured with Blakey for a few years, and was featured on Moanin, which is probably Blakey's best known recording. When Benny Golson left the Jazz Messengers, Morgan persuaded Blakey to hire Wayne Shorter, a young tenor saxophonist, to fill the chair. This classic version of the Jazz Messengers, including Bobby Timmons and Jymie Merritt would record the classic The Freedom Rider album.