Internet of vehicles (IoV) is an emerging paradigm for accommodating the requirements of future intelligent transportation systems (ITSs) with the overwhelming trend of equipping vehicles with versatile sensors and communications modules, and facilitating drivers and passengers with a variety of innovative ITS applications. However, the implementation of IoV still faces many challenges, such as flexible and efficient connections, quality of service guarantee, and multiple concurrent support requests. To this end, in this paper we introduce the software-defined IoV (SD-IoV), which is able to tackle the above-mentioned issues by adopting the software-defined networking framework. We first present the architecture of SD-IoV and develop a centralized vehicular connection management approach. Then, we aim to allocate dedicated communications resources and underlying vehicular nodes to satisfy each service. We formulate the dynamic vehicular connection as an overlay vehicular network creation (OVNC) problem. A comprehensive utility function is also designed to serve as the optimization objective of OVNC. Finally, we solve the OVNC problem by developing a graph-based genetic algorithm and a heuristic algorithm, respectively. Extensive simulation results are provided to demonstrate the effectiveness of our proposed solution of dynamic vehicular connection management.