The Browns have a bye this week and then will host the Baltimore Ravens for a Monday night game in Week 12.
Manziel has started the team's last two games, in Cincinnati and in Pittsburgh. He was filling in for Josh McCown, who's been dealing with a rib injury. The Browns dropped both games but head coach Mike Pettine said he was impressed with how Manziel had been progressing.
"I just thought the improvement that he made from the Cincinnati game to this one, it was a leap," Pettine said Monday, via the Browns' website. "Given what he has gone through, you are just proud of the kid and happy for him. Wish we had a better result from a team standpoint because -- pardon my French -- he played his ass off."
Manziel completed 33 of his 45 passes for 372 yards in Cleveland's 30-9 loss Sunday to the Steelers, an impressive recovery from 15-for-33 performance one week earlier against the Bengals. He especially improved in his reads. Against Pittsburgh, he threw one touchdown and one interception and was 29-for-35 for 282 yards from the pocket, according to ESPN Stats & Info.
Manziel this season has completed 59.4 percent of his passes and thrown five touchdowns and two interceptions. The Browns are 1-2 in his three starts this year.
This decision to move forward with Manziel as the starter represents a reversal of Pettine's position last week when he said McCown would start when he was healthy again.
On Monday, McCown seemed prepared for Manziel to take over the starting job.
"I will support and help him get ready just like I did this week and do everything I can to help him to play the best ball he can to help us win football games," McCown said Monday. "That is the way I view it -- any player on a team, you do everything you can to help the team win and to serve the team in your role."
McCown, who signed a three-year contract with the Browns in the offseason, has completed 65 percent of his passes this year and thrown 11 touchdowns and four interceptions.
At 2-8, Cleveland is currently in position for the top pick in the 2016 NFL Draft. The final weeks of this season might be the best chance for the Browns to determine whether Manziel, a 2014 first-round pick, can be their quarterback of the future.