Born in St. Louis, Missouri, Osby studied at Howard University, then at the Berklee College of Music.

[1] He moved to New York City in 1982, where he played with Jaki Byard, Jim Hall, Muhal Richard Abrams, Andrew Hill, Jack DeJohnette, Dizzy Gillespie, and Herbie Hancock.

[2] With Geri Allen, Steve Coleman, Gary Thomas, and Cassandra Wilson, he was a founding member of the M-Base Collective.

[2] He gave exposure to young pianist Jason Moran,[4] who appeared on most of Osby's 1990s albums, including Further Ado, Zero, Banned in New York and Symbols of Light, a double quartet featuring the addition of a string quartet to the band.

[7] Nate Chinen, writing for The New York Times, called Osby "a mentor and a pacesetter, one of the sturdier bridges between jazz generations," and stated that he has "a keen, focused tone on alto saxophone and a hummingbird's phrasing, an equilibrium of hover and flutter.