Content prefetching brings contents close to end users before their explicit requests to reduce the content retrieval time, which is crucial for mobile scenarios, such as vehicular ad-hoc networks (VANETs). In order to make intelligent prefetching decisions, three questions have to be answered: which content should be prefetched, when and where it should be prefetched. This paper answers these questions by proposing a vehicle mobility prediction-based over-the-top (OTT) content prefetching solution. We proposed a vehicle mobility prediction module to estimate the future connected roadside units (RSUs) using data traces collected from a real-world VANET testbed deployed in the city of Porto, Portugal. We designed a multi-tier caching mechanism with an OTT content popularity estimation scheme to forecast the content request distribution. We implemented a learning-based algorithm to proactively prefetch the user content to VANET edge caching at RSUs. We implemented a prototype using Raspberry Pi emulating RSU nodes to prove the system functionality. We also performed large-scale OpenStack experiments to validate the system scalability. Extensive experiment results prove that the system can bring benefits for both end-users and OTT service providers, which help them to optimize network resource utilization and reduce bandwidth consumption.