Deng will hold a player option on the 2015-16 season, a source said.
Deng chose the Heat believing their returning nucleus and free-agent signings can keep them contending in the Eastern Conference. The absence of state income tax made the Heat's offer a sound financial decision for him, too.
Heat president Pat Riley and Deng's agent Ron Shade talked on Saturday and completed the deal on Sunday morning.
Deng, 29, delivers the Heat a tough-minded, defensive-first forward with a versatile offensive game to complement Chris Bosh on the frontline.
For Deng, the deal gives him a chance to return to free agency next summer in what could be a stronger financial market for him. Between Chicago and Cleveland, Deng averaged 16 points and 5.7 rebounds.
Miami has been determined to reshape the roster into contention without James. Riley signed Bosh to a five-year, $118 million contract, and is nearing deals with Dwyane Wade, Udonis Haslem and Chris Andersen, sources told Yahoo Sports. Miami plans to also sign free agents Danny Granger and Josh McRoberts.
Deng met with Riley and coach Erik Spoelstra in Chicago last week to discuss a deal with the Heat.
More NBA coverage:
- Sports & Recreation
- Luol Deng
- Miami Heat
- LeBron James