Demps, who will turn 32 in June, has played in 107 games with 41 starts over nine seasons with the Eagles (2008-09), Texans (2010-12), Chiefs (2013), Giants (2014) and Texans (2015-16). He was selected by Philadelphia in the fourth round of the 2008 NFL Draft out of UTEP.
Demps, who didn't make his first NFL start until his sixth season in the league in 2013 with Kansas City, has recorded 15 of his 18 career interceptions the past four seasons, including six in 13 games last year with Houston.
The Bears struggled mightily in the secondary last year, especially at safety. Their defense intercepted just eight passes and generated only 11 takeaways, the fewest in team history.
In January, Bears general manager Ryan Pace discussed the importance of improving in that key aspect of the game.
"I honestly think we need to add more playmakers to our secondary," Pace said at the time. "We need to add more ball skills to our secondary. That's on me and we'll do that."
Demps has also averaged 26.6 yards with two touchdowns on 110 kickoff returns, but he has only had more than 12 returns in two seasons with 52 in 2008 and 33 in 2013.
At UTEP, Demps registered 17 career interceptions, the second most in school history and his three interception return TDs were tied for the most.