The $13.5 million contract nets Demps $5 million in his first year, per ESPN’s Adam Caplan.
Demps, who turns 32 in June, played in and started 13 games for the Texans last season and had six interceptions to go along with nine passes defensed and 55 tackles. In 14 games (13 starts) in 2015, Demps had six passes defensed and a pick.
In 2014, Demps played in all 16 games with nine starts for the Giants and had four interceptions. He picked off four passes as a member of the Chiefs in 2013.
The Bears will be Demps’ fifth team in his NFL career, which began with the Eagles in 2008 as a fourth-round pick out of UTEP.