Mundy appeared in 16 games (nine starts) for the New York Giants last season, where he recorded a career-high 70 tackles, one sack and one interception. The 6-foot-1, 209-pound safety played four years (2009-12) for the Pittsburgh Steelers, starting five combined games during that stretch.
Mundy was selected by the Steelers in the sixth round of the 2008 NFL draft out of West Virginia.
With Major Wright expect to depart via free agency, Mundy should fill one of the Bears’ safety spots in 2014.
Although Chris Conte struggled last season, the Bears will allow the former third-round draft choice to compete for a starting job in the preseason.