"He's obviously a talented young man to have been the 10th pick in the draft," Texans coach Gary Kubiak told the team's official Web site. "Those things happen in this business, and it's a chance for him to get a fresh start.
"We're getting a very smart player who has been productive, and we'll see if we can kind of get the motor going again and all that back. So it's a nice try for us as a football team and it makes us deeper at the quarterback position."
The Texans were looking for insurance at backup quarterback after Dan Orlovsky threw two interceptions in Houston's last preseason game last week. The Texans cut backup quarterback John David Booty, another former USC quarterback, over the weekend despite his two touchdown passes in the preseason finale.
The Cardinals took Leinart with the No. 10 overall pick in the 2006 draft, after he guided the Trojans to two national championships and a third title-game appearance.
The Associated Press contributed to this report