The deal is worth $26 million, a source told ESPN.com's Pierre LeBrun.
Dubnyk was traded three times in the past two seasons, moving twice in 2013-14 and once last season -- from the Arizona Coyotes to the Wild in January.
The 29-year-old goalie was electric upon joining Minnesota, setting a franchise record with 38 consecutive starts and compiling a 27-9-2 record for a team that made a furious climb to a playoff berth.
In the first playoff appearance of his six-year career, Dubnyk helped the Wild to the second round, in which they were dispatched by the Blackhawks. He had a .908 save percentage, a 2.52 goals-against average and one shutout.
Dubnyk was in line for a sizable free-agent contract after playing for just $800,000 on the one-year deal he signed with Arizona before last season.