Unmanned Aerial Vehicle (UAV)-enabled wirelessly powered Mobile Edge Computing (MEC) is emerging as a powerful technology for boosting computational capability and energy supplementation in Internet of Things (IoT). This work addresses the long-term task completion ratio maximization problem in UAV-enabled wirelessly powered MEC systems. Besides the large number of optimization parameters, the environment can only be partially observed as the UAVs cannot cover the whole network area. Then, it is very challenging to obtain good solutions due to the lack of global information. We introduce a novel distributed Multi-Agent Deep Reinforcement Learning (MADRL) framework for optimizing UAVs’ actions and resource allocation, considering the constraints of tasks that vary in size, arrival times, and required computation completion time. To decouple the complicated parameters, we divide the problem into two manageable subproblems—UAVs’ action decision and resource allocation under a given UAV’s action. We employ a distributed Deep Reinforcement Learning (DRL) scheme for the former subproblem to cope with the partially observable nature. By revealing some important properties of the later subproblem, we design an efficient two-stage optimal algorithm to minimize the total consumed energy of nodes while maximizing the task-completing number. Extensive simulations validate the effectiveness of the proposed framework, achieving over a 50% improvement in task completion ratio compared to baseline schemes in some scenarios.