Official, being reported by major news outlets.
For the record, I don't think this is good news. He is part of the whole SEC! SEC! SEC! mystique. Saban leaving would have been a step toward bringing that conference down toward the others, both in perception and reality.
Update: Kevin McGuire at NBC Sports is reporting Mack is staying, but I'm not seeing other reports of that.
Update #2: Bobby Burton of 247Sports also reporting Mack will stay on as coach.