Boudreau, 61, will sign a four-year contract worth almost $12 million, according to reports.
In five seasons with the Ducks, Boudreau was 208-104-40. He also coached the Washington Capitals from 2007-12 and won the 2007-08 Jack Adams Award. He is 409-192-80 in nine NHL seasons.
After Boudreau was fired by the Capitals on Nov. 28, 2011, he was hired by the Ducks two days later. Boudreau joins the Wild eight days after being fired by the Ducks.
He reportedly interviewed with the Ottawa Senators on Friday.
Torchetti went 15-11-1 for Minnesota. The Wild were eliminated in six games by the Dallas Stars in the Western Conference First Round of the Stanley Cup Playoffs.
Anaheim was eliminated by the Nashville Predators in the first round.