The deal is for $16 million, with $9 million guaranteed, Schefter reported.
Graham, 33, played for the Packers for the past two seasons. He had 38 catches for 447 yards and three touchdowns in 16 games, including 10 starts, in 2019.
Graham is a five-time Pro Bowler, with his most recent such honor coming in 2017. He has 649 catches and 74 touchdowns in his 10-year NFL career.
Tight end was one of the Bears' biggest weaknesses in 2019, as Trey Burton couldn't stay heathy and Adam Shaheen continued to disappoint. No Bears tight end registered 100 receiving yards for the season in its entirety.
While the legal tampering period opened to get free agency underway Monday, signings and trades can't become official until the new league year begins Wednesday at 3 p.m. CT.