Houston eventually confirmed the move on Wednesday.
Weeden was waived by the Dallas Cowboys on Tuesday to make room for Tony Romo, who has returned from a broken collarbone.
The Texans were in need of depth at the quarterback position. Before Houston claimed Weeden, Deepi Sidhu of HoustonTexans.com announced T.J. Yates would start for the Texans on Sunday and practice squad quarterback Zac Dysert would be his backup if Brian Hoyer, who is battling a concussion, was unable to go.
Rapoport later indicated Hoyer is likely out for Sunday's game against the New York Jets, which prompted the team's move.
Weeded told reporters on Thursday he could play Sunday if he had to, but said it's difficult to learn a brand new system this fast, according to Aaron Wilson of the Houston Chronicle.
"It's a great opportunity and everybody I've talked to raves about how good this locker room is," Weeden said, per the team. "It's been crazy. Got the call and was extremely excited. It's been a whirlwind."
Weeden continued to say he felt he'd put the Cowboys in position to win games, but was disappointed in the lack of wins in Dallas, per Tania Ganguli of ESPN.
Weeden never lived up to the expectations that surrounded him when the Cleveland Browns took him in the first round of the 2012 draft. He played 15 games during his rookie season and threw for 3,385 yards but had 14 touchdowns to 17 interceptions while the Browns finished 5-11 in another lost campaign.
Cleveland released him after the 2013 season, and the Dallas Cowboys signed him in 2014 to a two-year contract for depth purposes.
Weeden started three games while Romo was out and threw for one touchdown and two interceptions on his way to losses in each contest.
Matt Cassel replaced him as the starter in Week 6 and proceeded to lose four straight games himself.
Weeden is 32 years old, and at this point in his career, he's not much more than a journeyman quarterback who can serve as a backup or injury replacement. It is unrealistic to expect an immediate turnaround for the former Oklahoma State Cowboy under center, even with a new team.
At least he adds some depth to an injury-riddled position.
At 4-5, the Texans still remain tied with the Indianapolis Colts for first place in the AFC South.