In nine games last season, the 34-year-old Jones registered 23 tackles, four passes defended and one interception.
He also averaged 21.8 yards on six punt returns.
One of the games Jones sat out last season was the result of a suspension stemming from a January 2017 arrest. Jones pleaded guilty to obstructing a police officer and served two days in jail.
He was a First Team All-Pro in 2014 as a return man, and he was named to his first and only Pro Bowl in 2015.
In 139 career regular-season games, Jones has 16 interceptions and five punt-return touchdowns to his credit.
Cleveland has overhauled its secondary this offseason by selecting cornerback Denzel Ward with the No. 4 overall pick in the 2018 NFL draft and signing free-agent corners E.J. Gaines, Terrance Mitchell and T.J. Carrie.
The Browns also have a quality holdover in Briean Boddy-Calhoun.
Jones would provide some additional cornerback depth, and he could potentially serve as the Browns' primary return man.