Skrine has six career interceptions, including four last season in his second full year as a regular starter with Cleveland.
Terms weren't immediately available. The person spoke to The Associated Press on condition of anonymity because the deal Tuesday hadn't been announced by the team.
The 25-year-old Skrine was a fifth-round draft pick of the Browns out of Tennessee-Chattanooga in 2011.
He drew the ire of Browns fans at times because of inconsistency, but the Jets jumped at improving their secondary as they await a decision by Darrelle Revis, their former star cornerback who's a free agent after helping New England win the Super Bowl.
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