GATSim is a novel urban mobility simulation framework that leverages generative agents to overcome the limitations of traditional rigid rule-based systems and mimic complex and adaptive human mobility behavior. It leverages large-scale language models and AI agent technologies to generate agents with diverse socioeconomic profiles, individual lifestyles, and preferences that evolve through psychologically informed memory systems, tool usage, and lifelong learning. Key features include an architecture that integrates an urban mobility-based model, an agent-cognitive system, and a traffic simulation environment, a hierarchical memory system that includes spatial and temporal associations, keyword matching, and semantic relevance, and an innovative planning and response mechanism that models adaptive mobility behavior by incorporating multi-scale reflection processes. The implemented system demonstrates that generative agents generate realistic and consistent mobility behaviors, and outperform human annotators with a posterior probability of 92%. The source code is publicly available.