There was some talk that Denver could make the switch and go with Paxton Lynch but he’s still working his way back from a shoulder injury that has kept him sidelined and has yet to practice more than a few times.
Denver made the decision to bench Trevor Siemian last week after a poor outing against the Chiefs.
Osweiler, 26, is a former second-round pick of the Broncos in 2012. He played out his rookie contract with the Broncos before signing a four-year, $72 million contract with the Texans that included $37 million guaranteed back in March of last year.
The Texans traded Osweiler and a 2018 second-round pick to the Browns in return for a 2017 fourth-round pick.
Cleveland had been attempting to trade Osweiler since they acquired him several months ago but the ultimately cut him loose coming out of the preseason after no deal surfaced. The Broncos signed him to a contract soon after.
In 2017, Osweiler has appeared in two games and completed 21 of 42 passing attempts (50 percent) for 226 yards to go along with one touchdown and two interceptions.