The 27-year-old Conley was the Jets’ regular punter in 2011. He ranked 30th in the NFL in gross average (42.7 yards) and 18th in net average (38.8). The Jets released him last September, replacing him with Robert Malone.
Conley was most recently with the Vikings, who released him in April after signing him in January. The Vikings are going with rookie Jeff Locke at punter.
The Browns did not have a punter with regular-season experience on the roster until the reported agreement with Conley. Reggie Hodges, their punter in 2012, is an unrestricted free agent.
The Browns begin OTAs on Tuesday.