Mayfield led Cleveland to its first victory since 2016 on Thursday night.
Baker Mayfield was named the Browns' starting quarterback on Monday, the team announced.
Cleveland head coach Hue Jackson met with the Browns' quarterbacks on Monday to alert them of the change from Tyrod Taylor to Mayfield.
Mayfield entered Cleveland's Thursday night contest with the Jets late in the second quarter, replacing Taylor, who suffered a concussion.
The No. 1 pick in 2018 quickly made an impact by throwing for 201 yards while completing 73.9% of passes. Mayfield engineered a 21-17 comeback victory and gave the Browns their first win since December 2016.
"[Mayfield] made some tremendous throws," Jackson said on a conference call on Friday. "Obviously, he was able to move the team. Played with some rhythm. Got the ball into the playmakers' hands and gave them chances to make plays."
The 2017 Heisman Trophy winner will make his first NFL start on Sept. 30 by heading to Oakland for a road matchup with the Raiders. Kickoff from O.co Coliseum in Oakland is slated for 4:05 p.m. ET.