Terms were not disclosed.
Mitchell likely will compete with Derek Ross and Pete Hunter, who were both rookies last year, for the starting left cornerback spot in Dallas.
"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 because of injuries to Andre Dyson and Samari Rolle.
Mitchell, who grew up in Beaumont, Texas and attended SMU, becomes just the second free agent defensive player to sign with the Cowboys, joining linebacker Al Singleton.