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.
Morgan tried to move in to the more advanced areas of the music in the early 1960s. He left the Jazz Messengers in 1961, struggling with heroin addiction, managing to kick his habit in his hometown. He returned to the music scene after a two-year absence, playing on Grachan Moncur III's essentially avant-garde Evolution album (his favourite work), and experimenting on some of his own recordings such as the title track of Search for the New Land (1964), but the popularity of his famous album, The Sidewinder, featuring Joe Henderson precluded his career developing in this way.