The deal had been rumored in recent days, but the Timberwolves had to clear salary cap room, which came when Wesley Johnson was traded to Phoenix on Friday.
"I'm excited to be returning to the NBA with the Minnesota Timberwolves," Kirilenko said in a release. "The Wolves have one of the best coaches in the league in Rick Adelman, and I feel my game fits in well with his style of play. I also like the talent that Minnesota has on the team with star players like Kevin Love and Ricky Rubio."
Kirilenko was an All-Rookie team selection with Utah in 2002 and was an All-Star in 2004.
"Over his time in the NBA he has proven to be one of the best defensive players in the world," Timberwolves president of basketball operations David Kahn said in a release. "His ability to play multiple positions and big-game experience will be wonderful assets to our team ... We are excited to see him in a Timberwolves uniform."