Connected and autonomous driving is developing rapidly in recent years. However, current autonomous driving systems, which are primarily based on data-driven approaches, exhibit deficiencies in interpretability, generalization, and continuing learning capabilities. In addition, the single-vehicle autonomous driving systems lack of the ability of collaboration and negotiation with other vehicles, which is crucial for the safety and efficiency of autonomous driving systems. In order to address these issues, we leverage large language models (LLMs) to develop a novel framework, AgentsCoDriver, to enable multiple vehicles to conduct collaborative driving. AgentsCoDriver consists of five modules: observation module, reasoning engine, cognitive memory module, reinforcement reflection module, and communication module. It can accumulate knowledge, lessons, and experiences over time by continuously interacting with the environment, thereby making itself capable of lifelong learning. In addition, by leveraging the communication module, different agents can exchange information and realize negotiation and collaboration in complex traffic environments. Extensive experiments are conducted and show the superiority of AgentsCoDriver.