The trade was made to help facilitate the Bulls' impending signing of Dwyane Wade. The Cavs will use a trade exception to acquire Dunleavy, who is under contract for $4.8 million next season.
Cleveland is likely to send Chicago a second-round pick or the rights to a player overseas, sources said.
Dunleavy, whom the Cavs chased in free agency last summer, was excited about the deal, sources said. He averaged 7.2 points and shot 39 percent on 3-pointers for the Bulls last season, in which he was limited to 31 games after back surgery.
LeBron James has long coveted the versatile Dunleavy as a teammate.
Meanwhile, veteran swingmanRichard Jefferson announced Wednesday via Snapchat that he will return to Cleveland on a two-year deal.Jefferson, 36, said after the Cavs won the title that he would call it a career, but he changed his mind at the team's victory parade in downtown Cleveland and made it official Wednesday night.
Chicago shipped point guard Jose Calderon to the Los Angeles Lakerson Wednesday in another deal to clear salary-cap space, league sources told ESPN.
Information from The Associated Press was used in this report.