Later Friday, Dragic confirmed the agreement with a post on social media.
"I'm glad that I can announce that I'm staying with my #HeatNationFamily," Dragic wrote on Twitter. "Let's finish the job we started!"
The 34-year-old Dragic will be entering his seventh season with the Heat. He averaged 16.2 points per game while coming off the bench in last year's regular season. He cracked the starting lineup in the playoffs, but he tore his plantar fascia in Game 1 of the NBA Finals against the Los Angeles Lakers to dampen Miami's title hopes.
Leonard, the No. 11 overall pick in the 2012 NBA Draft, averaged 6.1 points and 5.1 rebounds per game for the Heat this past season.