The Heat and the 29-year-old point guard from Ljubljana will execute the new contract on 9 July, which is the first day players can officially sign new contracts, according to ESPN.
Dragić will thus stay with the Florida team, which traded with the Phoenix Suns for him alongside his younger brother Zoran in February.
Once Dragić signs the contract, he will become the owner of the richest deal in Slovenian sports ever. His previous deal in the world's best basketball league was US$30m and lasted four years.
Dragić has been one of the most coveted guards in this year's free agency in the NBA after winning the Most Improved Player award and making it to the All-NBA third-team last year.
Even though the Slovenian has secured a new contract in the NBA, he is unlikely to play for the national team at the Eurobasket in September for personal reasons. He is to become a father for the second time in August.