Groves played last season for the Cleveland Browns, appearing in five games and recording four total tackles, two sacks and two forced fumbles. He will be reunited with Titans defensive coordinator Ray Horton, who was also with Cleveland last season.
Groves, 30, was in training camp with the Houston Texans this year before being released.
He was originally drafted by the Jacksonville Jaguars in the second round of the 2008 NFL Draft and has 157 tackles, six forced fumbles and two interceptions in six NFL seasons.
- Scooby Axson