From ESPN Chicago's Jeff Dickerson:

In the end, Chicago proved to be the best fit for Corey Graham.
After testing the free agent market, Graham agreed to a new one-year contract with the Bears.

Good news to start the day. Corey Graham was always and should have always been a priority. And now the Bears had to sign him after losing 2 good special teams players in Rashied Davis (Lions) and Danieal Manning (Texans). The Bears will now match Graham, who some people consider is the best punt coverage man in the league, with new free agent acquisition Sam Hurd to give the Bears arguably the best duo of punt coverage men in the NFL. Graham had 25 solo tackles on special teams last year while Hurd had 19 playing with the Dallas Cowboys.

It seemed like Graham was heading elsewhere where he could battle for a starting CB position. But I guess he couldnt pass up the opportunity of being coached by Dave Toub.