Deng met with Heat president Pat Riley last week in Chicago and joins a team that is re-tooling on the fly in the wake of James' departure.
Deng turned down a three-year, $30 million offer from the Bulls in January before getting dealt to the Cleveland Cavaliers. The Bulls avoided the luxury tax with the deal, made in the wake of Derrick Rose's knee injury.
Deng turned down the Bulls' take-it-or-leave-it offer as much for the tenor of the negotiations than the monetary value. In the summer of 2013, the Bulls tabled contract extension talks and then approached Deng with their final offer before making the move to acquire Andrew Bynum's contract, which got waived.
Deng, 29, is a two-time All-Star who will join Chris Bosh and the imminent re-signings of Dwyane Wade and Udonis Haslem. Riley previously received verbal commitments from Josh McRoberts and Danny Granger.