Cleveland will receive Deng in exchange for center Andrew Bynum and three future draft picks sent to the Bulls.
The Team GB star, 28, could be on his way again in six months' time, as he becomes a free agent at the end of the season.
Chicago will also have the right to swap 2015 first-round picks with the Cavaliers.
"We are very excited for Luol to join the Cavaliers organization," Cavaliers general manager Chris Grant said in a statement.
"He's a tremendous defensive player that can impact the game on both ends of the court with a team first mentality and is a high character leader."
The Bulls are expected to release Bynum in a move that will give them financial flexibility and help them build for the future once franchise player Derrick Rose returns from his lengthy injury absence.
Cleveland will add the 28-year-old Deng to a young roster that is currently outside of the Eastern Conference playoff race.
The Briton, who has missed time recently with a sore Achilles, has averaged 19 points and 6.9 rebounds for the Bulls this season.
Deng has spent his entire career in Chicago, playing through many play-off battles while reaching the All Star Game the last two seasons.
There is no some doubt as to whether the London-based forward will play for Great Britain in the summer’s European Championship qualifiers because due to insurance issues.