There was no further information provided by the school. He missed the 2016 season after being ruled academically ineligible.
Griggs, who is returning from offseason Achilles surgery, threw for 1,879 yards with 16 touchdowns and two interceptions last season, while rushing for 270 yards and three more scores.
In his first season as starter, Griggs guided Southern Miss (8-5) to a 5-5 record in games that he played, including a 42-13 loss to Florida State in the Independence Bowl.
Southern Miss opens the season on Sept. 1, hosting Jackson State.