In an interview with TMZ Sports on Wednesday, Brown said, "He's a gunslinger, he can throw the ball, he's got a great attitude, he's young. I like everything about him."
Five months later, Brown admitted he may have been wrong to doubt the selection: "They didn't go with what everybody said, including myself. They went with what they thought was correct, and I really appreciate being able to say to them, 'I guess you were right.'"
Mayfield saw his first game action last week when veteran quarterback Tyrod Taylor exited the game against the New York Jets with a concussion.
Cleveland was trailing 14-0 when Mayfield entered the game, but it went on to secure a 21-17 victory and its first win since 2016.
Mayfield went 17-of-23 for 201 yards with no touchdowns and no interceptions and caught a successful two-point conversion.
Head coach Hue Jackson subsequently named him the starting quarterback.
The Browns are 1-1-1 and coming off an 0-16 season, but Brown believes they "absolutely" have a chance to win the AFC North.
Cleveland will look to take another step toward that goal Sunday when it faces the Oakland Raiders on the road.