Vickerson, 32, had 12 tackles in 15 games for the Chiefs last season. He is expected to give the Jets depth on the defensive line after Kenrick Ellis signed with the Giants as a free agent. Defensive tackle Leger Douzable is also a free agent.
Vickerson also has been with Miami, Tennessee, Seattle and Denver during his 10-year career. He has 165 career tackles, 6 1/2 sacks, two forced fumbles and an interception.
Vickerson was a seventh-round pick of the Dolphins out of Michigan State in 2005.
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