The former North Carolina defensive end, the 16th overall pick, will receive a fully guaranteed deal, according to a league source, for about $9 million.
The contract includes the standard team option for a fifth year.
"(I want to show) that I can compete at the highest level, that I can compete on the national stage, that I can help the New York Jets get to a Super Bowl," Coples said at the recent rookie minicamp.
With Coples signed, the Jets have six of their eight draft picks under contract.
Coples was named a starter at the conclusion of the draft, with coach Rex Ryan also saying he expects Coples to be an every-down player. On passing downs, the 6-foot-6, 284-pound lineman will slide inside, rushing alongside former No. 1 pick Muhammad Wilkerson.
Coples will replace Mike DeVito in the starting lineup. Soon after the draft, the Jets approached DeVito about restructuring his contract, which has only one year remaining. He wound up accepting a $610,000 pay cut. He will earn a guaranteed $2.5 million in 2012, with a chance to recoup the lost money with incentives.
Before his senior year, Coples was projected as a top-five pick, but his stock dropped after a lackluster season that raised questions about his desire and work ethic. Ryan flew to Coples' pro day to work him out personally and came away impressed. The Jets got their first extended look at him in last weekend's rookie minicamp.
"He's got all of it," Ryan said during the minicamp. "He's got range. He's got length. He uses his hands on a pass-rush. He can flip his hips, do all that type of stuff. ... I really feel there might be more to give. I think he might even have upside, so I thought that was a terrific pick."
The Jets expect Coples to add more athleticism to their defense, which slipped to fifth in yards allowed after finishing first and third in 2009 and 2010, respectively. With Coples and Wilkerson, who played together in 2007 at the Hargrave Military Academy in Virginia, the Jets upgraded the quality of their defensive line in the last two drafts.