ESPN.com's Adam Schefter reports that the deal is worth $33 million with a $12 million signing bonus.
The deal was reportedly reached before midnight, thereby preventing Brackett from entering the free-agent market.
Bracket, a defensive captain since the 2007 season, has made 99 or more tackles every season since 2005, and that's despite missing four games in 2008 (99 tackles) and two games last year (also 99 tackles).