Motorsport.com revealed late last month that Cook had taken leave from the team amid rumours that a permanent exit was on the cards.
That exit has now been confirmed with Cook no longer part of the newest team in Supercars.
As initially reported team owner Peter Xiberras will take over the team principal role for the time being.
Cook joined PremiAir from Triple Eight shortly after the former Tekno/Team Sydney squad was purchased by Xiberras.
His departure coincides with the arrival of another ex-Triple Eight employee, with Romy Mayer recently joining PremiAir's engineering department.
