A league source told ESPN NFL Insider Adam Schefter that it's a one-year deal.
Benson, 29, spent the past four seasons with the Cincinnati Bengals, rushing for more than 1,000 yards each of the past three years. His best season came in 2009, when Benson ran for 1,251 yards and six touchdowns.
But Cincinnati showed little interest in re-signing the eight-year veteran.
The fourth overall pick out of Texas in the 2005 draft, Benson spent his first three seasons with the Chicago Bears.
The Packers have been plagued by injuries in what has been an unimpressive running game. Green Bay finished 27th in rushing in 2011 despite going 15-1.
Information from ESPN's Chris Mortensen and The Associated Press was used in this report.