Schaub was Houston's starter from 2007 until last season, when he was benched in favor of Case Keenum after a terrible start to the year. The Texans were expected to contend for a Super Bowl last season, but instead became the NFL's worst team, sinking to 2-14, which tied the worst record in franchise history.
It was clear after last season that Schaub didn't have a future in Houston, but his departure looked to be imminent on Thursday night when the Texans signed veteran quarterback Ryan Fitzpatrick.
Houston also has the first overall pick in this year's draft, which includes top quarterbacks Teddy Bridgewater, Blake Bortles and Johnny Manziel.
While the Texans had plenty of problems last season, Schaub's poor play was perhaps the biggest. The Texans won their first two games before Schaub began to struggle and he threw six interceptions, three of which were returned for touchdowns in the next three games. He started the sixth game of the season and left with an injury before being replaced in the starting lineup by Keenum, an undrafted free agent who spent 2012 on the practice squad.
Keenum was injured late in the season, forcing Houston to go back to Schaub for the last two games. He didn't fare any better than he had before he was benched and he threw four interceptions combined in the last two games as Houston wrapped up the season with a 14-game skid.
The 32-year-old is a two-time Pro Bowler, who last made the game in 2012. He had been solid for the Texans since taking over the job after being traded from Atlanta in 2007, but his best seasons came in 2009 and 2012 when he started each game. In 2009, he led the NFL in yards passing (4,770), completions (396) and attempts (583) and was fifth in touchdown passes (29). In 2012, he threw for 4,008 yards with 22 touchdowns and 12 interceptions to help Houston to its second straight AFC South title.
He spent three seasons with the Falcons as Michael Vick's backup before joining the Texans, and has thrown for more than 24,000 yards with 130 touchdowns in his 10-year career.
The Associated Press contributed to this report