League sources told ESPN that Teague has agreed to a three-year, $57 million contract with the franchise.
Teague agreed to the deal at the start of NBA free agency at 12:01 a.m. Saturday.
He joined the Pacers in a three-team trade, which included George Hill going to the Jazz and the Hawks getting the No. 12 overall pick in the 2016 NBA Draft.
The point guard averaged 15.3 points and career highs in assists (7.8) and rebounds (4) last season. The 2014 All-Star also started 82 games.
Teague's new pact includes a third-year player option. He will be paired with the Timberwolves' other big-name offseason acquisition, Jimmy Butler in what looks like an explosive young offense.