Brown, 26, was a third-round draft pick of the Pittsburgh Steelers in 2011 out of the University of Texas.
The Jets announced the signing Tuesday.
Brown has 49 total tackles, two passes defensed and one forced fumble in 34 NFL games, with no starts. He tore the anterior cruciate ligament in his left knee in November 2013 and was released by the Steelers last March. Brown did not play last season.
Brown's uncle, Hosea Taylor, played three NFL seasons as a defensive end with the Baltimore Colts from 1981-83.
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