With the move, Goligoski returns home. The defenseman is from Grand Rapids, Minnesota, and played three seasons for the University of Minnesota.
"It's home. Everyone has that desire to play for their home state at some point," Goligoski told reporters. "I think it's a great fit for me."
The 35-year-old veteran hasn't shown the offense the past few seasons that he flashed earlier in his career, but he was still responsible in his own end and ate up minutes for the Arizona Coyotes, finishing second in ice time last season.
He had three goals and 22 points last season. Overall, he has 83 career goals and 429 points in 924 career games.
Goligoski won a Stanley Cup with the Pittsburgh Penguins in 2009. After six-plus years with the Dallas Stars, he signed a five-year contract with Arizona and was supposed to be one of the building blocks in the team's turnaround.
The Coyotes, however, are hitting the reset button after making the playoffs only once in the past nine seasons.
In other moves, the Wild signed Frederick Gaudreau to a two-year, $2.4 million deal on Wednesday. Forward Dominic Turgeon and defenseman Jon Lizotte signed one-year, two-way contracts with the team, and defenseman Joe Hicketts was given a two-year, two-way deal.