Mobile edge computing (MEC) has been envisioned as an essential technology for latency-critical applications by providing computing services in close proximity to mobile users. Bringing MEC to come into practice, how to support user mobility remains challenging. In addition to seeking a thorny trade-off between service latency and migration cost, both interactions in space and time exist in mobility management, which requires collaboration among users and perfect prior knowledge, including user mobility and network information. In this paper, we propose an efficient mobility management framework for MEC networks, in which mobility management is operated centered around users’ performance and cost, while radio access and computing service provision are loosely coupled. With a loosely coupled design, the proposed framework exhibits more flexibility and incurs higher complexity. Focusing on multi-user and multi-cell MEC networks, this joint control problem is formulated to maximize the long-term total utility accounting for the service delay and migration cost. Considering the exponential complexity, a distributed mobility management approach is developed, which combines game theory and user-oriented deep reinforcement learning to deal with the interactions in space and time. Simulation results show the efficiency and scalability of the proposed approach.