Adelman and the Timberwolves had reached an agreement in principle about two weeks ago.
The 20-year coaching veteran will take over a languishing franchise hinging its hopes to a young group led by All-Star forward Kevin Love.
The 65-year-old Adelman has a 945-616 career record during head coaching stints in Portland, Sacramento, Golden State and Houston. He left the Rockets this past April.
"After a thorough search and interview process, we're pleased to be bringing a coach of Rick Adelman's stature on board to coach the Minnesota Timberwolves," said David Kahn, Timberwolves president of basketball operations. "Rick has proven time and again that he is one of the top coaches in basketball -- one of the top coaches in the history of our sport. We are excited to have him as the leader of our young and talented team."
Adelman led Portland to a pair of NBA Finals appearances (1990, '92) and has guided his clubs to the playoffs 16 times.
"I'm eager to start another chapter in my coaching career with the Minnesota Timberwolves," Adelman said. "We have a good nucleus of young players that I feel can grow together and win. I'm looking forward to the challenge of building a playoff team here in Minnesota."