Multi-access Edge Computing represents a key enabling technology for emerging mobile networks. It offers intensive computational resources very close to the end-users, useful for task offloading purposes. Many scientific contributions already proposed approaches for optimally allocating these resources over time. However, most of them fail to take advantage of the prediction of both users’ mobility and service demands over a look-ahead temporal horizon. To bridge this gap, this paper formulates a novel methodology for anticipatorily allocating communication and computational resources at the network edge, based on the prediction of spatio-temporal dynamics of mobile users. The conceived architecture exploits a Software-Defined Networking approach to monitor users’ mobility, a Convolutional Long Short-Term Memory to predict over different look-ahead horizons the number of users within a given number of cells and their related service demands, and Dynamic Programming to optimally allocate users’ requests among available Multi-access Edge Computing servers. Computer simulations investigate the effectiveness of the proposed approach in a realistic autonomous driving use case and compare its behavior against a baseline solution. Obtained results demonstrate its unique ability to dynamically and fairly distribute users’ requests among the resources available at the network edge, while ensuring the targeted quality of service level.