ESPN.com's John Clayton first reported the deal Thursday. According to a source, the Bengals inserted language in the contract -- which covers two seasons -- to protect themselves in case Jones gets in trouble off the field.
The Bengals said in a news release that Jones would practice with the team Tuesday.
Cincinnati also announced on Monday the signing of safety Gibril Wilson, who had 91 tackles for the Miami Dolphins last season. Wilson's one-year deal is slightly above the league minimum of $630,000 but it also includes incentives.
Jones, who was released by the Cowboys after the 2008 season and didn't play last year, worked out for the Bengals twice this offseason, including last Tuesday. He was selected by Tennessee in the first round of the 2005 draft, but has struggled to stay on the field because of his repeated arrests.
Jones, 26, was suspended for the entire 2007 season and for six games with the Cowboys in 2008 for violating the NFL's conduct policy.
Jones could have some trouble making the Bengals. Cincinnati has one of the best cornerback tandems in the league in Johnathan Joseph and Leon Hall, who had six interceptions apiece last season. Morgan Trent, a sixth-round pick last year, had a solid rookie season, and the Bengals selected Brandon Ghee from Wake Forest in the third round last month, looking for depth at the position.
The defense finished fourth in the league in 2009, one of the main reasons Cincinnati won the AFC North with a 10-6 record.
Jones was expected to be a cornerstone of Tennessee's defense for years after he was drafted out of West Virginia. Instead, he was arrested six times and involved in 12 instances requiring police intervention. The Cowboys traded for him and he got into trouble again, drawing the six-game suspension for an alcohol-related scuffle with a team-provided bodyguard.
He appeared in nine games with Dallas, starting six, but failed to get an interception. He also returned punts and averaged only 4.5 yards, prompting the Cowboys to release him after the season.
Jones went to West Virginia along with late Bengals receiver Chris Henry. The two of them got into so much trouble with their NFL teams that commissioner Roger Goodell toughened the league's disciplinary policies.
The Bengals released Henry in 2008 following his fifth arrest. Owner Mike Brown referred to himself as a "redeemer" and did an about-face, bringing Henry back against the wishes of coach Marvin Lewis. Henry died in a fall from a pickup truck driven by his fiancee late last season.
The Bengals became more cautious about signing troubled players after they had 10 arrested during a 14-month span. Henry and linebacker Odell Thurman were the main offenders, drawing repeated suspensions beginning in 2005.
The team has softened its stance in the last two years, bringing in players on low-risk deals. Running back Cedric Benson was released by the Bears after two alcohol-related arrests -- the cases were dropped after grand juries declined to indict -- and the Bengals signed him to a minimal financial deal during the 2008 season.
They took the same approach last season with running back Larry Johnson, who got a minimal contract and left as a free agent after the season.
In February, the Bengals signed receiver Matt Jones, who didn't play in the NFL last season, to a one-year deal at close to the league minimum. Jones was charged with cocaine possession and with violating a plea agreement, prompting the Jaguars to release him after the 2008 season.
ESPN.com senior NFL writer John Clayton and The Associated Press contributed to this report.