Landry spent his first five NFL seasons with the Washington Redskins after he was picked No. 6 overall in the 2007 draft out of LSU. The hard-hitting Landry had a number of teams interested in him despite finishing last season on injured reserve with an Achilles injury.
ESPN reported Monday that the deal was for $4 million.
Landry will slide in as a starter in a secondary that was in serious need of help at the safety position. New York also had Reggie Nelson in for a visit, but he chose to return to Cincinnati.