Benson's deal is worth $3 million, with another $2 million attainable in incentives, a source told ESPN.com senior NFL writer John Clayton.
The 28-year-old Benson was the focal point of a running game that helped the Bengals win the AFC North title in 2009. The Bengals decided to emphasize the passing game last season, a move that backfired as the Bengals stumbled to a 4-12 record. Still, he recorded his second straight 1,000-yard season with 1,111 yards.
He ran for 1,251 yards in 13 games in 2009, missing three because of a strained hip. He also set a club record by running for 100 yards six times. He also ran for 169 yards in a playoff loss to the Jets, a club record for the postseason.
Benson recently was arrested in Austin, Texas, on a misdemeanor count of assault with bodily injury with family violence. Benson's attorney Sam Bassett said in a statement the arrest followed "a conflict" between Benson and a male former roommate.
The Chicago Bears, who selected Benson fourth overall in 2005, released him in 2008 after a pair of alcohol-related arrests in Texas. The cases were dropped when grand juries declined to indict.
Information from ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.