McCown was cleared Wednesday by an independent neurologist, the final stage before he can practice. The 13-year veteran had been expected to return last week but had a setback.
Browns coach Mike Pettine will discuss the team's decision at his 12:25 p.m. ET news conference Wednesday.
Manziel is returning to his backup role just days after getting the first win of his career. The 2012 Heisman Trophy winner, who has overcome personal issues since joining the Browns, threw two long touchdown passes in a 28-14 win over Tennessee on Sunday. He completed eight of 15 pass attempts for 172 yards but had two more fumbles, giving him four in two games.
Pettine said earlier this week that he would start the quarterback who gave him the best chance to win. He's comfortable with the 36-year-old McCown, who signed a three-year contract during the offseason and led the Browns on a 90-yard drive before he was hurt trying to launch himself into the end zone, getting hit by two Jets defenders on Sept. 13.
Pettine hinted Monday at going back to McCown and made it clear the Browns would not be swayed by the polarizing Manziel's status as a first-round pick.
McCown is 17-33 as a career starter and has deep knowledge of Cleveland's offense. While Manziel has made major strides, he remains a work in progress, and the Browns are more comfortable with the 22-year-old as a backup.
Information from The Associated Press was used in this report.