McCown suffered a concussion on the first drive in the season opener against the Jets and sat out last week against Tennessee because of lingering symptoms from the head injury.
"[McCown's] done everything that we've asked of him in the offseason, so far this year," Browns coach Mike Pettine said. "He'd earned the right to be our starting quarterback. We feel that he gives us the best opportunity to win on Sunday, and that truly was the basis for the decision."
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.
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.
"I am not going to sit here and say that I love the decision, but I respect coach Pett and that's the guy that makes the calls for this team," Manziel said. "I am going to be a team player and be ready when my number is called."
Manziel completed eight of 15 pass attempts for 172 yards against the Titans but had two more fumbles, giving him four in two games.
"[Manziel's] making great strides," Pettine said. "If he continues to make strides really, he can get where we all want him to be. But just where we are right now, we look forward to Josh leading the offense against the Raiders on Sunday."
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.
"This was a positive thing for us that our second quarterback went in and played well," Pettine said. "But there was a reason we started the season with Josh as the one and Johnny as the two. That was our plan, and at this point we're not seeing a reason to deviate from it."
Information from The Associated Press was used in this report.