NFL Network's Ian Rapoport first reported the decision.
On Sunday, coach Bill O'Brien said he would not put a timeline on his decision, saying he needed to wait until he was comfortable choosing a starter.
Less than 24 hours after making that statement, O'Brien has reportedly made up his mind.
Hoyer, 29, has played six seasons in the NFL for the Patriots, Cardinals and Browns. He started 13 games for the Browns last year, going 7–6 and throwing for 3,326 yards, 12 touchdowns and 13 interceptions.
Mallett, 27, was the less experienced option with just two starts over his four-year career, though he is considered a strong prospect.
Neither quarterback shined in the Texans' 14–10 loss to the Broncos on Saturday. Hoyer completed 7 of 11 passes for 52 yards, and Mallett completed 5 of 7 for 23 yards. Neither threw for a touchdown.
- Erin Flynn