The deal is worth $1.5 million, with incentives that can push it to $2 million, a source told ESPN.com Vikings reporter Ben Goessling.
Wootton entered the 2013 season as the starter at defensive end opposite Julius Peppers, but a rash of injuries on the defensive line forced him to play inside on occasion at defensive tackle.
A four-year veteran, Wootton underwent arthroscopic hip surgery in January, but is expected to fully recover in time to play in 2014. Wootton posted 35 tackles and 3.5 sacks last season after a 2012 campaign in which he produced a career-high seven sacks.
"I'm looking forward to being 100 percent recovered from this, to really showcase what I can do," Wootton said.
Wootton played in just 13 regular-season games over his first two seasons with the Bears due to multiple injuries, but has played in all 16 games over the past two years.
ESPN.com Bears reporter Michael C. Wright contributed to this report.