Stajan, a defensive specialist and key penalty-killer, was set to become an unrestricted free agent at the end of this season and had been rumored to be on the trade market.
Terms of the deal were not disclosed, but the Calgary Sun reported it was for $12.5 million.
The 30-year-old Ontario native has notched seven goals and 17 points in 41 games and is considered a team leader in the locker room.
Stajan has compiled 116 goals and 328 points over 693 career games.
Celebrity Families of 2014 [PHOTOS]