A free agent following Miami's memorable run to the Finals at Walt Disney World Resort in Orlando, Dragic opted to re-commit to the Heat on Friday.
Dragic's deal is reportedly for two years, with a team option in the second year.
In a Twitter post, Dragic wrote: "I'm glad that I can announce that I'm staying with my #HeatNationFamily.
"Let's finish the job we started!!! #LetsGoHeatnation #HeatNation #HeatFamily."
Dragic has called Miami home since being acquired from the Phoenix Suns in 2015.
The 34-year-old Slovenian – pick 45 in the 2008 NBA Draft – averaged 16.2 points, 5.1 assists and 3.2 rebounds per game last season as the fifth-seeded Heat eventually fell to the Los Angeles Lakers in the Finals.
Heat team-mate Meyers Leonard also reportedly decided to return to the Eastern Conference champions.
Leonard – who joined from the Portland Trail Blazers in 2019 – averaged 6.1 points, 5.1 rebounds and 1.1 assists per game last season.
Led by two-time reigning MVP Giannis Antetokounmpo, the Bucks are in championship mode after losing in the semi-finals last season, having fallen in the Conference Finals in 2018-19.
The Bucks are fortifying their postseason push by sending D.J. Augustin and D.J. Wilson to the struggling Rockets for Tucker and Rodions Kurucs, according to ESPN.
Milwaukee and Houston are also reportedly redirecting draft picks as part of the deal.
Tucker has been on the outer in Houston, where he and the Rockets agreed for the veteran to stay away from the team until a trade could be found.
The 35-year-old will bring playoff experience to the Bucks, having spent four years with the Rockets, which included a trip to the Western Conference Finals and back-to-back semi-final appearances.
Tucker has struggled in 2020-21, averaging career lows for points (4.4), field goal percentage (36.6) and three-point percentage (31.4) amid Houston's woes.
Meanwhile, the Miami Heat traded Meyers Leonard and a 2027 second-round pick to the Oklahoma City Thunder for Trevor Ariza.
Leonard – a part of Miami's run to last season's NBA Finals – will not be reporting to Oklahoma City and will not be an active member of the organisation, the Thunder said in a statement.
It comes after Leonard, who suffered a season-ending shoulder injury in February – was fined $50,000 by the NBA for an anti-Semitic slur last week.
Ariza – an NBA champion in 2009 – lands in Miami, having not played a game in a year after the 35-year-old opted out of the Orlando bubble amid the coronavirus pandemic in 2019-20.
