Jason La Canfora of CBS Sports first reported the news, adding his ankle injury "shouldn't be an issue."
On Thursday, ESPN also reported the move, noting that Watson took first-team reps in practice during the short week.
Watson, the team's first-round pick in this year's NFL draft, wasn't the Texans' starter heading into the regular season. But Tom Savage struggled dramatically in the team's 29-7 loss to the Jacksonville Jaguars in Week 1, losing two fumbles before being benched after the first half.
Watson promptly led the team on a touchdown drive, though his play was spotty after that, as he finished the game 12-of-23 with 102 yards, a touchdown, an interception and a lost fumble himself.
"The decision to go with Deshaun had more to do with could we find a spark, could we find somebody that could maybe make a play, that could escape the pocket, things like that," head coach Bill O'Brien said after the game, per Nick Shook of NFL.com. "I thought that Tom really hung in there and played very tough. We had a hard time protecting him so I just made the decision to go with Deshaun."
It appears that was a decision the team ultimately decided to stick with going forward, and it wasn't terribly surprising after Savage's poor performance.
Watson certainly provides the Texans with more mobility at the position, an issue for Savage on Sunday as he was sacked six times. Still, there will be an inevitable learning curve for Watson, as Savage provided far more experience in O'Brien's system.
But Watson was always going to be the future at the position for the Texans. That future seems to have become the present a bit more quickly than the Texans likely anticipated.