The deal was announced on Monday.
The 35-year-old Backstrom went 24-15-3 with a 2.48 goals against average, a .909 save percentage and two shutouts in 42 games last season for the Wild. He was hurt during warm-ups before the first-round playoff series began against the Chicago Blackhawks and unable to play in any of the games.
Backstrom tied for first in the NHL in victories and tied for fifth in the league in games played. His uncertain status made goaltending Minnesota's greatest off-season concern, but with backup Josh Harding still under contract the Wild can now concentrate on other positions this summer.