Nelson was also considering a deal from the New York Jets.
Nelson, a former first-round pick by Jacksonville, led the Bengals with four interceptions and ranked third in tackles last season. Nelson also broke up eight passes, forced two fumbles and recorded two sacks.
Nelson was the No. 21 overall pick in 2007 out of Florida. He has spent the past two seasons with the Bengals and was considered the second-best safety on the free-agent market, behind former Washington Redskins safety LeRon Landry.
Information from ESPN.com's Jamison Hensley contributed to this report.