Atlanta will receive two second-round choices and will move from 10th to eighth in the first round of this year's NFL draft as part of the agreement, the Houston Chronicle reported.
The newspaper said Schaub agreed to a six-year, $48 million contract with $7 million guaranteed.
Schaub served as a backup to Atlanta quarterback Michael Vick for three seasons and completed 84-of-161 passes for 1,033 yards with six touchdowns and six interceptions in his 38 career NFL games.
He was a third-round choice of the Falcons in the 2004 draft.
"Matt is our starting quarterback," Texans General Manager Rick Smith told the Chronicle. "Everybody here appreciates the contributions that David has made to this franchise and to this city. We are working with his representatives to find another place for him. He'll be excited about his opportunity and we all wish him the very best."