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 swingman Richard 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.
Information from The Associated Press was used in this report.