Brooks will compete with Tyus Jones to be the Wolves backup point guard behind Jeff Teague.
Brooks played for Thibodeau during the coach's final season in Chicago in 2014-15, appearing in all 82 games and averaging 11.6 points and 2.0 assists in 23 minutes a game.
He is the third former Chicago Bulls player to join Thibodeau for his second season in Minnesota: The Wolves acquired three-time All Star Jimmy Butler in a draft-night trade in June, and they signed Taj Gibson as a free agent in July.
He has been a full-time starter for just a single season in his nine-year career, but his most recent start came as a member of the Bulls.
Brooks also has 38 playoff games under his belt.
Brooks is something of an National Basketball Association journeyman who has played for the Houston Rockets, Phoenix Suns, Sacramento Kings, Denver Nuggets, Bulls and Indiana Pacers since he was a first-round pick out of OR in 2007. The Seattle, Washington native owns career averages of 10.1 points on 41.3% shooting and 3.1 assists in 21.6 minutes per game.