Fog computing is a new systematic paradigm which provides low latency enabled cloud services to mobile and Internet of Things (IoT) networks by provisioning the computation capability within the radio access network (RAN) assignable to mobile end users. In this letter, an energy optimal offloading scheme based on a probabilistic priority model of cloud tasks is investigated over fog computing networks. The optimization problem jointly minimizes the energy consumption of user equipment (UE) and the fog server. Simulation results show that the proposed joint UE and fog server energy optimization (JUFO) scheme provides a better performance compared to the conventional offloading scheme, which operates strictly within the determined delay bound.