Gipson, 29, is an eight-year NFL veteran who has played in 112 career games. He had 51 tackles and three interceptions for the Texans in 2019 but was released by Houston earlier this week.
A Pro Bowl selection in 2014, Gipson is the likely favorite to become a starting safety for the Bears alongside Eddie Jackson. Gipson began his NFL career when he joined the Browns as an undrafted free agent in 2012.