Gustavsson would have become an unrestricted free agent on July 1.
Gustavsson earned a 16-5-4 record last season with a .907 save percentage and 2.63 goals-against average.
Wings lose Peters to Hurricanes
Detroit Red Wings assistant Bill Peters was named head coach of the Carolina Hurricanes on Thursday.
Peters spent the last three seasons in Detroit, working primarily with the team's defensemen and penalty-kill units.
Before joining the Wings, Peters was the head coach of the American Hockey League's Rockford Ice Hogs, leading them to consecutive 40-win seasons and Calder Cup playoff appearances in 2008-09 and 2009-10.
Peters is the franchise's 13th head coach and the fourth since the team's arrival in North Carolina.