Gillespie died in 1993; his wife Lorraine died last year. The auction will take place in their Englewood home.
Among the items for sale are the jazz great's trademark bent trumpet; other instruments, including drums and a piano; records; sheet music; a collection of autographed posters and photographs; personal correspondence; jewelry; and awards, including a Grammy and a gold record.
One cymbal belonging to Gillespie is scrawled with the words "Here lies cymbal stolen from [drummer] Cozy Cole and nurtured by Dizzy for 25 years. R.I.P. 1973."
Gillespie played with Cab Calloway and Billy Eckstein before forming the first high-profile bebop group with saxophonist Charlie Parker in the 1940s; later, he led small groups and big bands, and was a pioneer of Afro-Cuban jazz. He became an American icon, recognizable for his puffed-out cheeks while playing and the bent trumpet (which he claimed allowed him to hear his own playing better) and beloved for his high-flying virtuosity and his humor on the bandstand.