Terms of the deal were not disclosed Sunday.
The 37-year-old Moorman spent his first 12 seasons in Buffalo, setting franchise records for gross punting average (43.8 yards), total punts (862) and punts inside the 20 (243).
Moorman replaces second-year punter Shawn Powell, who was cut after a poor performance in Thursday night's 37-24 loss at Cleveland. Coach Doug Marrone cited a lack of hang time.
Powell averaged 23.1 net yards and failed to land one inside the Browns 20. He also struggled angling punts away from Cleveland's Travis Benjamin, who returned seven punts for a franchise-record 179 yards, including a 79-yard touchdown.
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