Tom Brady and head coach Bruce Arians reportedly recruited Bernard after Cincinnati released him last week.
The veteran runner spent his first eight NFL seasons with the Bengals, who drafted him in the second round in 2013.
The North Carolina product is a proven pass-catching running back and adds versatility to the reigning Super Bowl champions. He's racked up at least 30 receptions in every season since entering the league.
Bernard rushed for 416 yards (3.4 per carry) and three touchdowns through 16 appearances in 2020. The 29-year-old also added 355 yards and three scores on 47 receptions.