Claiborne was an unrestricted free agent and the NFL Network reported that the Jets signed him to a one-year contract worth more than $5 million a week after releasing cornerback Darrelle Revis.
Claiborne, 27, was the sixth overall pick by the Dallas Cowboys in the 2012 NFL Draft. He has yet to appear in more than 11 games in a season after appearing in 15 games as a rookie.
He missed six games in 2013 with a dislocated left shoulder and a hamstring injury. In 2014, he missed 12 games due to a torn left patellar tendon.
Claiborne started 11 games in 2015 while dealing with hamstring and ankle injuries. Following the 2015 campaign, Claiborne was an unrestricted free agent but he returned on a one-year deal.
Claiborne still struggled with injuries, sitting out the last nine regular-season games with a groin injury. He played in the NFC divisional playoff loss to the Green Bay Packers but injured his rib.
In 47 regular-season games, Claiborne has four interceptions, 26 passes defensed, a forced fumble and four fumble recoveries.