A source told ESPN.com the deal is worth $1.5 million in salary plus another $250,000 in games-played bonuses that are tied to the team making the playoffs next season.
Sutton, 36, would have been an unrestricted free agent July 1 and several playoff-contending teams had him on their short lists ahead of the Feb. 27 trade deadline.
Sutton has appeared in 33 games with the Oilers this season, collecting three goals, six assists and 56 penalty minutes.
In 657 career games with San Jose, Minnesota, Atlanta, Ottawa, the New York Islanders, Anaheim and Edmonton, Sutton has 149 points (38 goals, 111 assists) and 1,161 penalty minutes.
Sutton has been suspended twice this season for a total of 13 games for separate illegal hits to the head of an opponent.
He is making $2.125 million this season.
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press was used in this report.