The deal is worth $2.3 million, league sources told ESPN.
Wade reported to the Cavaliers' evening practice session Wednesday.
Wade's relationship with LeBron James, cemented during four seasons and two NBA titles together with the Heat, pushed the Cavaliers past the Oklahoma City Thunder, San Antonio Spurs and Miami in pursuit of Wade.
"There's no better place to be right now to continue to play and compete at the highest level. Cleveland believes in my talents and what I can bring to a championship contender both as a player and leader. I look forward to reuniting and playing alongside my brother LeBron," the 12-time All-Star guard said in a statement. "We've already won two championships together and I hope we win a third."
James said after practice Wednesday that he was "happy" the Cavaliers "were able to keep [Wade] away from everybody else."
"It's a guy -- come on, man -- this is like one of my best friends. It's kind of like when you start school and you walk into the classroom and you're not quite sure who your classmates are and when you walk in there and one of your best friends is in there, you're like, 'Oh, yeah, this is going to be fun. It's going to be a good class.' That's the type of feeling I got," James said.
Wade agreed to a contract buyout with the Chicago Bulls on Sunday. Wade, 35, gave back $8 million of his $23.8 million 2017-18 salary to reach a buyout agreement with the Bulls, league sources said.
Wade said in his statement that he had "always dreamed of playing for the Chicago Bulls and I feel so fortunate to have fulfilled my dream this past year."
"I look forward to reuniting and playing alongside my brother LeBron. We've already won two championships together and I hope we win a third."
"The team is now heading in a different direction, which has made me reevaluate where I need to be in this phase of my career. Being a part of a team that is in the process of rebuilding doesn't align with where I want to be right now no matter how difficult that decision may be," he said.
He called the decision to leave his hometown team "an incredibly difficult decision."
"It meant so much to me seeing my mom on the sidelines cheering me on as a Bull. I am so proud of the work we have been doing in the community and we plan to continue these efforts. It's been an honor and a privilege to play for my hometown. Chicago holds a very special place in my heart and will always be home to me," he said.
Wade, a three-time NBA champion and MVP of the 2006 NBA Finals, will join a formidable Cavaliers roster with James, Kevin Love, JR Smith and Tristan Thompson. The Cavs will be without injured All-Star point guard Isaiah Thomas until at least January.
Wade averaged 18 points for the Bulls last season. In 14 seasons, he has averaged 23.3 points, 5.7 assists and 4.8 rebounds a game.