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A source confirmed that the sides had reached the deal, which includes an option for a fifth year, to NFL Network's Albert Breer later Thursday.
Financial terms were not disclosed, but as the No. 16 pick in the 2012 NFL Draft, the first four years of Coples' contract are expected to be worth around $8.9 million.
The 6-foot-6, 284-pound defensive lineman from North Carolina has the versatility to play both defensive end and defensive tackle. Coples had 17.5 sacks over his final two seasons with the Tar Heels and first-year Jets defensive line coach Karl Dunbar views Coples as "an awesome fit" in the team's "46" defense.
Coples is the eighth first-round pick from the 2012 NFL Draft to sign with his team, joining the Carolina Panthers' Luke Kuechly, the Buffalo Bills' Stephon Gilmore, the Seattle Seahawks' Bruce Irvin, the San Diego Chargers' Melvin Ingram, the Chicago Bears' Shea McClellin, the Green Bay Packers' Nick Perry and the New York Giants' David Wilson. With Coples signed, third-round linebacker Demario Davis and seventh-round wide receiver Jordan White are the Jets' two unsigned draft choices.