Canadian-born Belfour, 42, will join the team at the start of the season in October, Leksand said on its website.
"I see it as an honour to play in a classic club like Leksand," Belfour said, adding he was lured to Sweden by "the adventure and the challenge."
Belfour became a free agent in July after spending last season with the Florida Panthers. He has previously played for the Toronto Maple Leafs, Chicago Blackhawks, San Jose Sharks and Dallas Stars.
Belfour won the Vezina Trophy as the NHL's top goalie in 1991 and 1993 and posted the leagues best GAA in four seasons. He also won a gold medal playing for Canada in the 2002 Winter Olympics.