In modern network environments, the exponential growth in data traffic and architectural complexity has made the centralized management of Software-Defined Networks (SDNs) increasingly challenging. Traditional SDN controllers, while programmable, still depend on static rules and human intervention for policy definition and threat mitigation, limiting their responsiveness in dynamic and large-scale deployments. This paper introduces a Large Language Model (LLM)-based agentic framework designed to enhance the cognitive and autonomous capabilities of SDN control planes. By integrating advanced reasoning and contextual understanding from LLMs, the proposed system enables intelligent policy generation, adaptive network reconfiguration, and explainable decision-making in real time.The framework leverages Mininet for virtual SDN simulation, Suricata as a telemetry and event-generation layer, and a multi-agent LLM pipeline for interpreting network events, classifying contextual significance, and dynamically generating flow rules. These rules are executed through an OpenDaylight SDN controller, allowing the network to respond automatically to anomalies, performance degradations, or security events without manual intervention. This closed-loop automation demonstrates how LLM-driven reasoning can transform SDN architectures from reactive, rule-based systems into proactive, self-optimizing infrastructures. The proposed approach supports continuous adaptation, scalability across cloud and IoT environments, and transparency through human-readable reports, marking a step toward fully autonomous and explainable network orchestration.