The team also announced Tuesday it waived tight end Nick Truesdell to make room on the roster.
Cooper has played in 74 games, including 28 starts, in stints with San Francisco, Kansas City, Arizona, Chicago and Detroit in six NFL seasons. He was released by the Lions on Monday.
The 2013 seventh-round draft pick out of Rutgers has seven career interceptions with 36 passes defensed and 154 tackles.
The Jets need experience and depth at the position after losing No. 1 cornerback Trumaine Johnson to a hamstring injury that could sideline him the rest of the preseason. Promising rookie Kyron Brown is also dealing with an injured hamstring after he had worked his way into the mix to start.
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