This paper considers an energy harvesting (EH) based multiuser mobile edge computing (MEC) system, where each user utilizes the harvested energy from renewable energy sources to execute its computation tasks via computation offloading and local computing. Towards maximizing the system's weighted computation rate (i.e., the number of weighted users' computing bits within a finite time horizon) subject to the users' energy causality constraints due to dynamic energy arrivals, the decision for joint computation offloading and local computing over time is optimized {\em over time}. Assuming that the profile of channel state information and dynamic task arrivals at the users is known in advance, the weighted computation rate maximization problem becomes a convex optimization problem. Building on the Lagrange duality method, the well-structured optimal solution is analytically obtained. Both the users' local computing and offloading rates are shown to have a monotonically increasing structure. Numerical results show that the proposed design scheme can achieve a significant performance gain over the alternative benchmark schemes.