The growing demand of industrial, automotive and service robots presents a challenge to the centralized Cloud Robotics model in terms of privacy, security, latency, bandwidth, and reliability. In this paper, we present a `Fog Robotics approach to deep robot learning that distributes compute, storage and networking resources between the Cloud and the Edge in a federated manner. Deep models are trained on non-private (public) synthetic images in the Cloud; the models are adapted to the private real images of the environment at the Edge within a trusted network and subsequently, deployed as a service for low-latency and secure inference/prediction for other robots in the network. We apply this approach to surface decluttering, where a mobile robot picks and sorts objects from a cluttered floor by learning a deep object recognition and a grasp planning model. Experiments suggest that Fog Robotics can improve performance by sim-to-real domain adaptation in comparison to exclusively using Cloud or Edge resources, while reducing the inference cycle time by 4times to successfully declutter 86% of objects over 213 attempts.