With the rapid increase in the amount of exchanged traffic over cellular networks, stemming partly from computation-intensive tasks, and the highly mobile nature of the users, mobility management exhibits considerable challenges in next-generation cellular networks. A way to alleviate these problems is by using Software-defined Radio Access Networks (SD-RAN), where a centralized controller with a complete overview of the network topology (distribution of users across base stations and their channel conditions) can make decisions on the user assignment and resource allocation. To that end, in this paper, we formulate an optimization problem with the objective of maximizing the network utility, where computation-intensive tasks are sent from the users to edge clouds, taking into account the communication constraints (uplink and downlink bandwidth) as well as the finite storage and processing capabilities of edge clouds. Moreover, we provide a user rate guarantee to satisfy an additional application for all users. The problem is NP-hard, therefore, we propose to use Deep Reinforcement Learning (DRL) to solve it. Extensive realistic simulations show that our approach is close to the optimal solution, where the latter is obtained using a solver, while outperforming a benchmark by up to 65%.