Cincinnati also signed defensive end Derrick Harvey, a free agent who played for the Broncos last season.
Jones has played five years in the NFL, and will enter his third season with the Bengals. He was sidelined with a neck injury last season, but still played in eight games, including the last seven as a starter. He had 31 tackles.
In January, Jones pleaded guilty to a misdemeanor charge of disorderly conduct. A second misdemeanor charge of resisting arrest was dismissed in a plea agreement with prosecutors. He may still face discipline from the league.
Collins has played all four of his seasons with Cincinnati, and Harvey played three seasons in Jacksonville before signing with Denver.