Benson left Cincinnati after spending four seasons with the Bengals, leading them in rushing each year. But Cincinnati showed little interest in re-signing the eight-year veteran.
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.
The 29-year-old Benson rushed for at least 1,000 yards in each of the last three seasons. He was Chicago's top draft pick in 2005.