Kiffin's departure leaves Owls coach and brother Lane Kiffin without the two coordinators who helped guide the team to a Conference USA championship this past season.
Kendal Briles left FAU to become the offensive coordinator at Houston. He was replaced by 24-year-old Charlie Weis Jr.
Both Lane and Chris are sons of Monte Kiffin, who serves as a defensive assistant at FAU.
Chris Kiffin has spent most of his coaching career in the college ranks, with stints at Idaho, Nebraska, USC, Arkansas State, Ole Miss and FAU.
News of his move to the 49ers was first reported by Sports Illustrated.