Brown replaces Skip Peete, who was let go after the 2012 season. Peete was later hired by the Chicago Bears.
Brown spent the last five seasons as the running backs coach of the Cleveland Browns.
Last season under Brown, No. 3 overall pick Trent Richardson rushed for 950 yards and 11 touchdowns, tying a franchise record for a rookie with three 100-yard games.
Brown takes over a unit that finished 31st in the NFL in rushing with 1,265 yards, the lowest in a 16-game season in franchise history. DeMarco Murray led the Cowboys with 663 rushing yards on 161 carries in 2012. However, he missed six games with a severely sprained foot.