Computation-aware delay optimal mobility management (MM) is an important problem in ultra-dense network (UDN) with mobile edge computing (MEC). Since the additional time delay caused by task computation is not taken into consideration, traditional radio access-oriented mobility management scheme cannot guarantee the overall delay performance of delay-sensitive user equipment (UE). In this paper, we propose a novel dynamic programming-based mobility management (DPMM) scheme to minimize the average delay under an energy consumption constraint. DPMM makes MM decisions using statistic information to handle the inaccurate state information. Cooperative data transmission is adopted to improve the delay performance. Simulation shows that the proposed DPMM scheme can achieve delay performance close to optimal and reduce the frequency of handover. However, the wireless link, computation resources and UE’s location in UDN environment is dynamic, which leads to information uncertainties. We further propose an MM scheme based on deep Q-network (DQN) to learn the system information from the environment. In this scheme, UE takes the current and past observed delay as experience, learning the optimal mobility management strategy through DQN training. Simulation shows that DQN-based MM can learn from experience and reduce the handover frequency to a certain degree.