Ian Rapoport of NFL Media reports that the Texans have claimed Morris and added him to their 90-man roster.
Morris spent just under a month with the Seahawks and has spent time with five other teams since entering the league as an undrafted free agent in 2014. He did not get into a regular season game with any of those teams.
With Morris in the fold, the Texans now have four quarterbacks on their roster. Brandon Weeden and Joe Webb both signed with the team as free agents this offseason and will be in the mix for the No. 2 job behind Deshaun Watson.