The LB started 27 straight games for Hilltoppers, was named first-team, Al-Conference USA this season
Barrett will play for the Golden Flashes in 2018, have three years of eligibility remaining.
Moore, a former Louisville assistant, spent the past four seasons at Central Michigan.
McClendon will not spend his final season of college football as a backup to Ryan Finley.
Shirreffs will have two seasons of eligibility remaining.