The agreement, which contains a player option for the third year, was struck as NBA free agency opened Saturday at 12:01 a.m. ET.
That freed up cap space for Minnesota to be aggressive in free agency, and Teague was a target.
Teague's steady play helped push the Pacers into the Eastern Conference playoffs, with Indiana ultimately getting swept by the Cleveland Cavaliers in the first round.
He was acquired before last summer's draft in a three-team deal that sent George Hill to the Jazz and the 12th pick in the draft to the Hawks.
Teague has missed just 17 games over the past four seasons.
He was ranked No. 10 on the list of top available free agents this offseason compiled by ESPN's Kevin Pelton.
ESPN's Ohm Youngmisuk contributed to this report.