Mobile-edge computing (MEC) enhances the capacities and features of mobile devices by offloading computation-intensive tasks over wireless networks to edge servers. One challenge faced by the deployment of MEC in cellular networks is to support user mobility. As a result, offloaded tasks can be seamlessly migrated between base stations (BSs) without compromising the resource-utilization efficiency and link reliability. In this paper, we tackle the challenge by optimizing the policy for migration/handover between BSs by jointly managing computation-and-radio resources. The objectives are twofold: maximizing the sum offloading rate, quantifying MEC throughput, and minimizing the migration cost. The policy design is formulated as a decision-optimization problem that accounts for virtualization, I/O interference between virtual machines (VMs), and wireless multi-access. To solve the complex combinatorial problem, we develop an efficient relaxation-and-rounding based solution approach. The approach relies on an optimal iterative algorithm for solving the integer-relaxed problem and a novel integer-recovery design. The latter outperforms the traditional rounding method by exploiting the derived problem properties and applying matching theory. In addition, we also consider the design for a special case of "hotspot mitigation", referring to alleviating an overloaded server/BS by migrating its load to the nearby idle servers/BSs. From simulation results, we observed close-to-optimal performance of the proposed migration policies under various settings. This demonstrates their efficiency in computation-and-radio resource management for joint service migration and BS handover in multi-cell MEC networks.