"He did a really good job when he played," Mangini said on the team's website (www.clevelandbrowns.com).
McCoy will start Sunday's game at Cincinnati and home games against Baltimore and Pittsburgh, Mangini said.
The rookie has not played since spraining his left ankle in a November 21 loss to the Jacksonville Jaguars.
He gained the starting assignment in five earlier games when quarterbacks Jake Delhomme and Seneca Wallace were hurt, leading the Browns (5-8) to wins over the New Orleans Saints and New England Patriots.
McCoy, who enjoyed a fine college career with the University of Texas, has passed for 975 yards and three touchdowns with three interceptions in his first season.
Delhomme, the starter the past three games, has been troubled by interceptions, throwing a team-high seven this season.
(Writing by Gene Cherry in Salvo, North Carolina. To query or comment on this story email firstname.lastname@example.org)