Jones, 35, had been an unrestricted free agent since the Bengals didn't pick up his contract option in March. He spent eight seasons in Cincinnati from 2010 to 2017.
The two-time Pro Bowler only played in nine games last season between a groin injury and a one-game suspension by the NFL for a violation of the league's personal conduct policy because of an arrest last January.
Jones was drafted sixth overall in the 2005 NFL draft by the Tennessee Titans. The West Virginia product has 494 career tackles, three sacks, 16 interceptions, seven forced fumbles and 12 fumble recoveries. He has also returned 182 punts for 1,922 yards and 121 kickoffs for 3,147 yards.
The specific terms of the deal were not released.