Owner Bob McNair said the team plans to do that and the decision "wasn't difficult at all."
"He's really been one of the best quarterbacks in the league this year," McNair said. "We could see how good he was and he just needed the opportunity and this year we were able to protect him better and keep him on the field and he put the numbers up there."
Schaub led the league in yards passing with a franchise-best 4,770 in helping Houston (9-7) to its first winning record with a victory over New England on Sunday. His 4,770 yards are the sixth-most in NFL history.
The Texans were eliminated from the playoffs late Sunday night with the New York Jets' win over Cincinnati.
It was the first time Schaub had started every game since arriving in Houston after missing five games in each of his first two seasons with injuries.
Though the decision on Schaub's contract didn't have to be made until March, McNair said they decided to give it to him the first time it was discussed.
"It was a no-brainer, there's no way that we're not going to keep Matt," McNair said. "He's our quarterback and the team has confidence in him. He's shown great courage and you've seen when he's gotten injured, he's gone back out there and led his team. So he's really won the respect of his teammates and that's what you need."
Schaub was 24 of 39 for 303 yards and two touchdowns against the Patriots for his ninth 300-yard passing game of the season, tied for second most in league history.