Mendenhall, a former Steelers first-round pick, is coming off an injury-plagued 2012 season in which he picked up just 182 yards.
But in the three prior years he averaged 1,103 rushing yards and 10 touchdowns per season for Pittsburgh.
"Obviously, I know Rashard well from our time in Pittsburgh and I hold him in very, very high regard," Cardinals head coach and former Steelers offensive coordinator Bruce Arians said.
"As a running back he's the total package. He's a big, strong, every-down back with speed who can pass block and also catch the ball."
The Cardinals also announced they had signed cornerback Jerraud Powers, quarterback Drew Stanton, linebacker Lorenzo Alexander and safety Yeremiah Bell to contracts.