Mobile-edge computing (MEC) and wireless power transfer (WPT) have been recognized as promising techniques in the Internet of Things era to provide massive low-power wireless devices with enhanced computation capability and sustainable energy supply. In this paper, we propose a unified MEC-WPT design by considering a wireless powered multiuser MEC system, where a multiantenna access point (AP) (integrated with an MEC server) broadcasts wireless power to charge multiple users and each user node relies on the harvested energy to execute computation tasks. With MEC, these users can execute their respective tasks locally by themselves or offload all or part of them to the AP based on a time-division multiple access protocol. Building on the proposed model, we develop an innovative framework to improve the MEC performance, by jointly optimizing the energy transmit beamforming at the AP, the central processing unit frequencies and the numbers of offloaded bits at the users, as well as the time allocation among users. Under this framework, we address a practical scenario where latency-limited computation is required. In this case, we develop an optimal resource allocation scheme that minimizes the AP's total energy consumption subject to the users' individual computation latency constraints. Leveraging the state-of-the-art optimization techniques, we derive the optimal solution in a semiclosed form. Numerical results demonstrate the merits of the proposed design over alternative benchmark schemes.