Agents built on LLMs are increasingly deployed across diverse domains, automating complex decision-making and task execution. However, their autonomy introduces safety risks, including security vulnerabilities, legal violations, and unintended harmful actions. Existing mitigation methods, such as model-based safeguards and early enforcement strategies, fall short in robustness, interpretability, and adaptability. To address these challenges, we propose AgentSpec, a lightweight domain-specific language for specifying and enforcing runtime constraints on LLM agents. With AgentSpec, users define structured rules that incorporate triggers, predicates, and enforcement mechanisms, ensuring agents operate within predefined safety boundaries. We implement AgentSpec across multiple domains, including code execution, embodied agents, and autonomous driving, demonstrating its adaptability and effectiveness. Our evaluation shows that AgentSpec successfully prevents unsafe executions in over 90% of code agent cases, eliminates all hazardous actions in embodied agent tasks, and enforces 100% compliance by autonomous vehicles (AVs). Despite its strong safety guarantees, AgentSpec remains computationally lightweight, with overheads in milliseconds. By combining interpretability, modularity, and efficiency, AgentSpec provides a practical and scalable solution for enforcing LLM agent safety across diverse applications. We also automate the generation of rules using LLMs and assess their effectiveness. Our evaluation shows that the rules generated by OpenAI o1 achieve a precision of 95.56% and recall of 70.96% for embodied agents, successfully identify 87.26% of the risky code, and prevent AVs from breaking laws in 5 out of 8 scenarios.