Terms were not disclosed.
Mitchell will likely compete with Derek Ross and Pete Hunter, both of whom were rookies last year, for the starting left cornerback spot.
"I just want the chance to compete," Mitchell said. "I feel I can play in the slot or on the outside."
In Tennessee, Mitchell served primarily as a nickel back before he had the opportunity to start last year due to injuries to Andre Dyson and Samari Rolle.
Mitchell, who grew up in Beaumont, Texas and attended Southern Methodist University, becomes just the second defensive player to sign with the Cowboys, joining linebacker Al Singleton.