Finch's coaching staff also received extensions. Terms were not disclosed.
The Timberwolves finished seventh in the West after going 46-36 this season, Finch's second as coach, marking the seventh-best single-season record in franchise history. The Timberwolves led the NBA in points per game (115.9) for the first time in franchise history. They also led the NBA in 3-pointers made (1,211) and turnovers forced (1,339).
"They came to me. I think that shows the type of energy and commitment in the building. Everything's going in the right direction here. It's a fun time to be a part of the Timberwolves,'' said Finch, who was hired midway through the 2020-21 season to replace the fired Ryan Saunders.
Finch has a 62-61 record for the second-best winning percentage (.504) by a head coach in Timberwolves history. The late Flip Saunders (.521) is first.
"They're not always easy decisions in this business, but this one was a very easy one. Coach has been a terrific partner for me, and the results on the floor are clear,'' executive vice president for basketball operations Sachin Gupta said.
The 52-year-old Finch has been an assistant with Toronto, New Orleans, Denver and Houston.
"He's always communicating, making sure everybody's straight," guard Anthony Edwards said. "That's what you love about him.''
The Associated Press contributed to this report.