In Connected Autonomous Vehicles scenarios or CAV, ubiquitous connectivity will play a significant role in the safety of the vehicles and passengers. The extensive amount of sensors in each car will generate vast amounts of data that cannot be processed promptly by onboard units. Edge and fog computing are emerging solutions for remote data processing for autonomous vehicles, offering higher computing power, as well as the low latency required by autonomous driving. However, due to the highly distributed nature of fog and edge computing servers, CAV mobility may pose a challenge to keep services close to end-users and maintaining QoS. In this paper, we propose MOSAIC, service migration, and resource management algorithm for intra-tier and inter-tier communication in edge and fog computing. The proposed solution performs proactive migration of services based on mobility information, server resources, QoS, and network conditions. Simulation results show the efficiency of the proposed algorithm in terms of latency, migration failures, and network throughput.