The surge in mobile vehicles and data traffic in Vehicular Edge Computing and Networks (VECONs) requires innovative approaches for low latency, stable connectivity, and efficient resource usage in fast-moving vehicles. Existing studies have identified that utilizing digital twins (DTs) can effectively improve service quality in VECONs. However, it still faces substantial challenges posed by large-scale complex DT communications in sustaining real-time collaborative endeavors. In particular, within the dynamic VECONs, the decision regarding DT migration plays a pivotal role in sustaining the quality of services. In this paper, we propose an adaptive DT migration (ADM) algorithm to minimize the overall migration costs when DTs deliver services. Specifically, 1) We formulate ADM as a combinatorial optimization problem in VECONs, comprehensively considering communication latency and migration latency under complex DT communications, vehicular mobilities, and dynamic states of edges; 2) An ADM algorithm based on off-policy actor-critic reinforcement learning is proposed to make migration decisions. Moreover, the ADM agent employs warm-up policies to address exploration challenges in sparse state spaces; 3) Simulations based on real-world, large-scale urban vehicular mobility datasets demonstrate that our method outperforms existing algorithms by approximately 39% on average, and it can achieve results close to the optimal.