Zappe will serve as the Browns' backup quarterback against the Bengals on Sunday.
The Browns re-signed Zappe on Tuesday, Tom Pelissero of NFL Network reports.
The Browns waived Zappe on Monday, Ian Rapoport of NFL Network reports.
Zappe (coach's decision) is inactive but will serve as Cleveland's emergency third quarterback.
Cleveland signed Zappe to its active roster Wednesday.
The Browns will sign Zappe off the Chiefs' practice squad Tuesday, Tom Pelissero of NFL Network reports.
The Chiefs signed Zappe to their practice squad Wednesday, Jordan Schultz of BleacherReport.com reports.
The Patriots are slated to waive Zappe, Mike Reiss of ESPN reports.
Zappe completed 12 of his 20 pass attempts for 108 yards and ran once for six yards in Thursday's 17-3 preseason win over the Panthers.
With veteran newcomer Jacoby Brissett and 2024 first-rounder Drake Maye viewed as roster locks, Zappe figures to compete with rookie sixth-rounder Joe Milton and Nathan Rourke for slotting on the Patriots' depth chart, Andrew Callahan of the Boston Herald reports.