The deal has yet to be announced by the team. ESPNChicago.com first reported the deal earlier Saturday.
Hanie, 26, who played at Colorado State, spent the last three seasons in Chicago. He replaced an injured Jay Cutler in the 2010 NFC Championship Game and nearly rallied the Bears past the Packers. But he went 0-4 in place of Cutler last season, including a loss at Denver.
The Associated Press contributed to this report.