Newman will enter his 11th NFL season and second with the Bengals. He played his first nine seasons with Dallas after being drafted in the first round in 2003.
Last season, Newman led the Bengals in passes defensed with 14 and had two interceptions to raise his career total to 34.
Defensive coordinator Mike Zimmer says Newman is "the kind of guy we want back as we work to keep our defense together."
Cincinnati also has re-signed ends Robert Geathers, Michael Johnson and Wallace Gilberry, cornerback Adam Jones and linebacker Rey Maualuga from last year's defense.
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