The move comes on the same day as news that guard Jermon Bushrod is leaving the team to join the New Orleans Saints and center Mike Pouncey has requested to be released.
The Bears declined to pick up an $8 million option to retain Sitton, a four-time Pro Bowl selection, for the 2018 season on Feb. 20.
The 31-year-old missed the final two games of the 2017 season with an ankle injury and also battled through a rib injury. He said when his option was declined by the Bears that he still has "prime years left" and intended to keep playing.
He started 25 of the 26 games in which he played for the Bears after joining the team in 2016, playing both the right and left guard spots.
Sitton, who entered the league with the Packers in 2008, lined up at right guard the first five years of his career. In 2013, the Packers moved him to the left side, where he stayed until the 2017 season, when the Bears shifted him back to the right side.
He has started 137 of the 147 career games in which he has appeared.
ESPN's Jeff Dickerson contributed to this report.