Johnny Manziel started Week 2 in McCown's place and got his first career victory, 28-14 over the Tennessee Titans.
But head coach Mike Pettine said Wednesday the Browns are going with McCown, a 36-year-old who has started for the Buccaneers and Bears in the past two seasons but one with a long injury history.
McCown left his first start with the Browns, Week 1 against the Jets, when he was in a head-on collision at the goal line. McCown went airborne and lost the ball, leaving the game with a concussion, and was not cleared for Week 2.
"Josh has been outstanding,'' Pettine said in an interview with NFL Network. "Anybody that knows him just knows how genuine he is, how truly passionate he is about football and about his teammates, and just wanting to win regardless of what his role is. That was a big part of our discussion when he came in for his free agent visit, that he wanted to not only be considered to be the quarterback but also that he wanted to mentor the young guys in the room.
"He's exceeded those expectations. It's like having another coach in the room. Kevin O'Connell the quarterbacks coach does an outstanding job. John DeFilippo, his background with quarterbacks is well documented. The dynamic in that room - I spent a lot of time in there - is outstanding."