Jefferson (groin) signed a one-year contract with the Browns on Thursday, Scott Petrak of the Elyria Chronicle-Telegram reports.
Jefferson said Monday that he is recovering from surgery to repair two ruptures to his groin, Rich Cimini of ESPN.com reports.
Jefferson (hip) has been ruled out for the remainder of Sunday's game against Miami.
Jefferson hurt his hip in Sunday's Week 15 game against Miami and is questionable to return.
Jefferson had five tackles (one solo), including 1.5 sacks, in Sunday's 13-8 loss to the Falcons.
The Jets signed Jefferson on Thursday, Ethan Greenberg of the team's official site reports.
The Seahawks are slated to release Jefferson, Adam Schefter of ESPN reports.
Jefferson (illness) has been deemed active for Sunday's regular-season finale against the Rams.
Jefferson (foot) returned to Saturday's wild-card contest at Cincinnati, Tashan Reed of The Athletic reports.
Jefferson injured his foot during Saturday's wild-card game at Cincinnati.