The quarter of the free agent Case Keenum accepted a one-year agreement of a value of up to $ 3 million with the Bears, Adam Schefter de ESPN reports.
Keenum will help the mentor Caleb Williams in Chicago as he did for CJ Stroud in Houston.
Tyson Bagent and Austin Reed are the other quarters on the list behind Williams.
Keenum, who had been with the Texans in the past two seasons, has spent all last season in reserve injured after having injured the foot in a pre-season match against the Rams.
Keenum, 37, played for seven teams in 12 seasons, with the Bears of his eighth team in 13 seasons. He has 66 departures, going 30-36 with 15,175 yards per pass, 79 affected and 51 interceptions.
The Texans have Davis Mills as a backup of Stroud, with Kedon Slovis also on the list.