Miami have acquired three-time All Star forward Antoine Walker from Boston in a five-team, 13-player deal - the biggest trade in NBA history.
The Heat also get guard Jason Williams and forward James Posey from Memphis, while the Grizzlies receive guard Eddie Jones from Miami.
The 6ft 9in Walker averaged 19.1 points and nine rebounds a game last season.
He has signed a six-year $53m deal and will team up with Shaquille O'Neal, the NBA's most dominant big man.
Heat president Pat Riley said: "We feel like with this trade we traded a lot, but we got back three quality players.
"Antoine Walker is one of the very best, multi-faceted, versatile players in this game."
Jones started all 80 games played with Miami last season, averaging 12.7 points and a career-high 5.1 rebounds.
"Eddie Jones is an All-Star caliber player who has had a terrific NBA career," said Grizzlies president of basketball operations, Jerry West.
"He is a great three-point shooter who will make an immediate impact on our offense, while also serving as a solid defender in the backcourt."
Also included in the trade:
Miami gets guard Andre Emmett from Memphis and the draft rights to Roberto Duenas from New Orleans.
Boston receive Curtis Borchardt from Utah; from Miami, the Celtics get Qyntel Woods, the draft rights to 2004 second-round pick Albert Miralles; and two second-round draft picks and cash.
Memphis acquire guard Raul Lopez from the Jazz.
Utah receive center Greg Ostertag from Memphis.
New Orleans get forward Rasual Butler from Miami; 6ft 6in guard Kirk Snyder from Utah.