GATSim is a novel simulation framework that leverages large-scale language models and AI agent technologies to overcome the limitations of existing rule-based urban mobility simulations. GATSim agents have various socioeconomic attributes, personal lifestyles, and evolving preferences, and make mobility decisions through psychologically-informed memory systems, tool-using abilities, and lifelong learning mechanisms. It has a comprehensive architecture that integrates urban mobility-based models, agent cognitive systems, and traffic simulation environments, and has been proven to generate results similar to real human mobility behavior. In particular, it enables realistic behavioral adaptation over time through a reflective process that converts experience into generalized insights. Reproducibility has been ensured through the public prototype system code on GitHub.