Mobile edge computing (MEC) has been proposed as a promising solution, which enables the content processing at the edges of the network helping to significantly improve the quality of experience (QoE) of end users. In this article, we aim to utilize the MEC facilities integrated with time-varying renewable energy resources for charging/discharging scheduling known as green scheduling of on-move electric vehicles (EVs) in a geographical wide area comprising of multiple charging stations (CSs). In the proposed system, the charging/discharging demands and the contextual information of EVs are first transmitted to nearby edge servers. With instantaneous electricity load/pricing and the availability of renewable energy at nearby CSs collected by aggregators, a weighted social-welfare maximization problem is then solved at the edges using greedy-based algorithms to choose the best CS for the EV's service. From the system point of view, our results reveal that compared to cloud-based scheme, the proposed MEC-assisted EVs scheduling system significantly improves the complexity burden, boosts the satisfaction (QoE) of EVs' drivers by localizing the traffic at nearby CSs, and further helps to efficiently utilize the renewable energy across CSs. Furthermore, our greedy-based algorithm, which utilizes the internal updating heuristics, outperforms some baseline solutions in terms of social welfare and power grid ancillary services.