The move reunites Ramirez with Bears coach John Fox, whom Ramirez played for in Denver from 2011-14.
Fox said last week that he expected the Bears to pursue another free-agent offensive lineman with positional versatility. Ramirez has experience playing both guard and center.
The veteran Ramirez was traded from Denver to Detroit during the first night of the 2015 NFL draft, when the Broncos moved up to take Shane Ray and the Lions moved back to draft Laken Tomlinson, the player who eventually replaced Ramirez in the starting lineup with Detroit.
Ramirez appeared in all 16 games for Detroit last season, playing 463 snaps between guard and center.
He spent four seasons in Denver prior to his second stint in Detroit, including being the starting center for the Broncos in Super Bowl XLVIII, a game the Broncos lost to Seattle 43-8.
Ramirez was initially drafted by the Lions in 2007 with a fourth-round pick.
ESPN NFL Nation reporter Michael Rothstein contributed to this report