Iguodala also has agreed to a two-year, $30 million extension with Miami, sources said. The extension includes a team option.
Justise Winslow is part of the package headed to Memphis, sources told Wojnarowski. The forward has played in only 11 games for the Heat this season because of injuries. He's averaging 11.3 points, 6.6 rebounds and 4 assists.
In addition, Miami, Memphis and the Oklahoma City Thunder had been working on an elaborate three-team trade that would land the Heat both Iguodala and Danilo Gallinari but the Heat and Thunder have not been able to reach agreement, league sources told Wojnarowski. Therefore, Memphis and Miami are focusing on a two-team deal at this time.
In an interview with The Undefeated's Marc J. Spears on Wednesday night, Iguodala said he will take a physical for the Heat on Friday and will need "a couple of days" before he's ready to play.
Iguodala also said he's "really excited" to be joining the Heat and playing with Jimmy Butler, who had similar feelings.
"[He brings] winning. He knows how to do that on both sides of the ball. He's super smart. There's nothing he cannot do," Butler said after a 128-111 loss to the LA Clippers on Wednesday. "We got a lot of pieces, man. He's definitely going to add to that."
Iguodala, 36, hasn't played for the Grizzlies this season. Last summer, the Golden State Warriors sent the veteran swingman -- who is making $17.2 million in the final year of his contract -- and a lightly protected 2024 first-round pick to the rebuilding Grizzlies because Golden State needed to shed his salary to execute a three-team, sign-and-trade deal for All-Star guard D'Angelo Russell.
Iguodala was a crucial piece of the Warriors' three championships and five consecutive Finals appearances; he is considered one of the league's elite wing defenders and is an excellent passer and threat off the dribble.
He averaged 5.7 points, 3.7 rebounds and 3.2 assists as Golden State's sixth man last regular season. Those averages increased to 9.8 points, 4.3 rebounds and 4.0 assists during the playoffs, when Iguodala started the majority of the games.
ESPN's Brian Windhorst contributed to this report.