Schaub, who has a $14.5 million salary-cap figure and a $10 million base salary for 2014, became expendable when the Texans signed former Tennessee Titans quarterback Ryan Fitzpatrick to a two-year deal Thursday night.
Not long after Houston got Fitzpatrick, Oakland made its final pitch for Schaub.
"A fresh start can do a lot of things for a player and a team and I'm one of those guys," Schaub said. "Last year did not go as I had planned, given my prior nine years before that. I'm looking for a fresh start, I'm excited for the opportunity here."
"The quarterback position is the most important position on the football field," Allen said. "We feel very confident that Matt Schaub is the guy that can come in and lead this football team. And he's proven that he can do it in this league."
The Cleveland Browns also had expressed interest in Schaub, who could have been reunited with former offensive coordinator Kyle Shanahan. But the Raiders wanted Schaub more, according to a source.
The trade between Oakland and Houston, teams scheduled to pick in the top five in this year's draft, could affect how high quarterbacks will be selected.
Oakland will have Schaub, a veteran atop the team's offseason wish list and someone who reduces the pressure on the team to use its first-round pick -- No. 5 overall -- on a quarterback.
"We weren't going to let last season deter us from the player and the track record that he has shown over his career," offensive coordinator Greg Olson said. "He was our No. 1 target from day one, and it was just a matter of getting the deal done."
Houston, which holds the No. 1 overall pick, likely has an even greater need at the quarterback position after trading Schaub.
The Raiders have three other quarterbacks in Pryor, McGloin and Trent Edwards. Allen recently said he was not sure whether the team's quarterback of the future was in the locker room at the time.
After leading the Texans to AFC South Division titles in 2011 and 2012, Schaub struggled early last season before being benched in favor of rookie Case Keenum in October. The 10-year veteran regained the starting job in late December but could not help the Texans avoid finishing the season with a 14-game losing streak, the longest in franchise history.
"People look at Schaub and only look at his last year," said Raiders safety Charles Woodson, who officially signed his one-year contract to return earlier in the day.
"I think they base his career off of his last year. But I see a guy that, in my opinion, has been very steady. He's done some really good things throughout his time. Sometimes you just need a fresh start, a new set of circumstances to restart, to restart your history. Hopefully this is the place that he can get it done."
A two-time Pro Bowler, Schaub has eclipsed 4,000 passing yards three times in his career. The 32-year-old spent the past seven seasons as the Texans' starting quarterback.
ESPN.com Raiders reporter Paul Gutierrez and The Associated Press contributed to this report.