Jones worked out for the Broncos on Sunday morning. He has a history with Broncos coach Vance Joseph, who was the Cincinnati Bengals' defensive backs coach in 2014-15. Jones played for the Bengals from 2010 to 2017.
He became an unrestricted free agent after the Bengals told him that they were not going to pick up the option on his contract for the 2018 season, with the hope that the veteran would return in 2018 at a lesser price.
Jones, who turns 35 on Sept. 30, played in only nine games last season due to a combination of injury and a one-game suspension for a violation of the NFL's personal conduct policy because of an arrest last January.
The Bengals stuck by Jones through thick and thin in the eight years he has spent with them, even pledging their loyalty after Jones was arrested for allegedly pushing a security guard and failing to comply with law enforcement on Jan. 3, 2017 -- the first day of the offseason.
A video from the back of a police car showed Jones going on a tirade against the arresting officer and telling him "I hope you die tomorrow." Jones was suspended by the NFL for the Bengals' season opener after the incident.
He was charged with misdemeanor assault, disorderly conduct and obstructing official business, along with a felony charge of harassment.
The prosecutor declined to pursue a felony charge of harassment with a bodily substance for spitting on the hand of a nurse while being booked into jail. All other charges were dropped except obstructing official business, to which Jones pleaded guilty.
The Bengals signed Jones as a free agent in 2010 after his career was on a downward spiral due to numerous off-the-field issues that resulted in him being suspended for the entire 2007 season. But even though Jones has said he wants to play for several more years, he is on the older side for a cornerback and started to lose playing time early last season to William Jackson III, the Bengals' 2015 first-round pick.
Jones also doubled as a kick returner and had a punt return for a touchdown last season that was called back because of a block in the back by his teammate.
The Broncos also announced that they had waived linebacker Bo Bower.
ESPN's Katherine Terrell contributed to this report.