Cureton, 29, has played seven years in the NBA. The 6-foot 9-inch, 215-pound veteran spent three seasons in Philadelphia and three in Detroit before he was traded to Chicago.
He averaged 6.9 points and 5.3 rebounds in 43 games for Chicago this season.
The Clippers will give the Bulls a second-round pick if Cureton is on the Clippers' active roster at the start of the 1988-89 season. However, the Bulls will receive a third-round pick if he is not on the active roster.
Cureton is expected to join the Clippers Friday night for a game in San Antonio.