Later Tuesday, special teams standout and linebacker Blake Costanzo said he received a two-year deal from Chicago.
He has completed 1,296 of 2,131 passes for 14,417 yards, 74 touchdowns and 50 interceptions in his career.
The 27-year-old Costanzo, who had 12 tackles for the NFC West champion 49ers last season, said he is eager to join one of the best special teams units in the NFL.
"I'm excited to be a part of the team," Costanzo said in a text message.
His agent, David Canter, also tweeted the news.
"Congratulations to client (at)BlakeCostanzo51 for agreeing to terms on a new 2 year deal with the Chicago Bears."
Signed by the Bears in 2010 after spending his first four seasons in Indianapolis, Jennings has seven interceptions with 42 pass breakups and five forced fumbles in his career. Known as a solid run-stopping corner, he overtook Zack Bowman for a starting spot opposite Charles Tillman during the 2010 season.