Weeden is being added as a backup quarterback, but he carries more importance because the presumed starter is Deshaun Watson, who is coming off surgery to repair a torn ACL suffered Nov. 2.
Texans coach Bill O'Brien told James Palmer of NFL Media that Watson is ahead of schedule in his recovery, and he is expected to be ready for the start of the 2018 season. But it remains unclear when Watson will return to team workouts.
Weeden, 34, played for the Texans in 2015 and 2016 before being released in September 2017.
Weeden has not played in a regular-season game since the 2015 season. He has started 25 games in the NFL and his teams have a 6-19 record in those contests. However, he won his only start for Houston in 2015, completed 15 of 24 passes for 200 yards with one touchdown and one interception in a 34-6 victory over the Titans.
Weeden has experience in O'Brien's system.