Curry, 29, owns career averages of 13.3 points and 5.3 rebounds in 511 games with the Bulls and Knicks.
But injuries shorted his seasons in 2008-09 and 2009-10 and kept him out of the league last year. He was reportedly overweight when he worked out for the Heat this summer, but the seven-footer apparently worked enough off for Miami take a chance on him.
Curry was the fourth overall pick of Chicago on the 2001 draft.
Miami also signed center Mickell Gladness and guards Cameron Jones, Jeremy Wise and Terrell Harris who were all members of the NBA Developmental League at some point during their careers.