Addington, 47, had been Kurt Busch's crew chief but left after a tumultuous season-ending race a week ago in which the Penkse Racing driver launched into a profanity-laced outburst in the garage at Homestead-Miami (Fla.) Speedway.
NASCAR later levied a $50,000 fine on Busch for his actions.
"I know Steve well and I know how he goes about setting up a racecar," Stewart said in a statement. "He balances the technical part of our sport with the real-world experiences we get at the track, and that will allow for a smooth transition as we prepare to defend our title in 2012."
Addington has 16 career Cup wins, including two with Busch this year. Addington was also a onetime crew chief for Kyle Busch, Kurt's younger brother, at Joe Gibbs Racing and helped him win eight races in 2008 and 12 victories overall.
At Stewart-Haas Racing, Addington replaces Darian Grubb, a former Hendrick Motorsports engineer who became Stewart's crew chief in 2009 when Stewart became co-owner of his race team.
Grubb said he was told in October that he would not return to Stewart-Haas. Stewart struggled badly at times during the season but then won five of the 10 races in NASCAR's Chase for the Cup playoff and captured his third Cup championship.
"He's a great person and I know he'll continue to be successful in this sport," Stewart said of Grubb.
Kevin Harvick, who finished third in the standings behind Stewart and Carl Edwards, also recently announced that he would have a new crew chief in 2012, with Shane Wilson taking over the No. 29 Chevrolet for Gil Martin at Richard Childress Racing.
-- Jim Peltz
Photo: NASCAR crew chief Steve Addington at Martinsville (Va.) Speedway on Oct. 31. Credit: Jared C. Tilton / Getty Images