Unmanned Aerial Vehicles (UAVs) are increasingly used in defense, surveillance, and disaster response, yet most systems still operate at SAE Level 2 to 3 autonomy. Their dependence on rule-based control and narrow AI limits adaptability in dynamic and uncertain missions. Current UAV architectures lack context-aware reasoning, autonomous decision-making, and integration with external systems. Importantly, none make use of Large Language Model (LLM) agents with tool-calling for real-time knowledge access. This paper introduces the Agentic UAVs framework, a five-layer architecture consisting of Perception, Reasoning, Action, Integration, and Learning. The framework enhances UAV autonomy through LLM-driven reasoning, database querying, and interaction with third-party systems. A prototype built with ROS 2 and Gazebo combines YOLOv11 for object detection with GPT-4 for reasoning and a locally deployed Gemma 3 model. In simulated search-and-rescue scenarios, agentic UAVs achieved higher detection confidence (0.79 compared to 0.72), improved person detection rates (91% compared to 75%), and a major increase in correct action recommendations (92% compared to 4.5%). These results show that modest computational overhead can enable significantly higher levels of autonomy and system-level integration.