The Timberwolves also brought in Scott Layden as general manager. Layden was the San Antonio Spurs' assistant general manager after previously working in the front office for the New York Knicks and Utah Jazz.
Thibodeau signed a five-year deal worth approximately $10 million annually, US media reported.
Thibodeau's first NBA job was as an assistant to Bill Musselman during the Timberwolves' expansion season of 1989-90. Thibodeau was fired by the Bulls last summer after a falling out with management.
Timberwolves' interim coach Sam Mitchell was given his walking papers after the team finished 29-53 in 2015-16. He took over after former coach Flip Saunders died in October.