Bodine is the fifth of the eight draft picks to agree to terms in the last three days, leaving only first-round cornerback Darqueze Dennard, second-round running back Jeremy Hill and third-round defensive end Will Clarke unsigned.
The 6-foot-4, 310-pound Bodine made history during the draft when he became only the third player the Bengals have ever traded up to draft. Cincinnati moved up 12 spots to draft Bodine 111th overall by trading its 123rd and 199th picks to Seattle.
The other four draft selections who have signed are fifth-round quarterback AJ McCarron, sixth-round linebacker Marquis Flowers, seventh-round wide receiver James Wright and seventh-round cornerback Lavelle Westbrooks.
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