The rapid proliferation of Large Language Models (LLMs) has introduced critical operational and environmental challenges, as model training and inference consume enormous computational resources and generate substantial carbon emissions that conflict with the United Nations Sustainable Development Goals (SDGs), particularly SDG 7 (Affordable and Clean Energy), SDG 9 (Industry, Innovation and Infrastructure), and SDG 13 (Climate Action). However, LLMOps workflows remain largely manual, fragmented, and reactive, while the Artificial Intelligence (AI) industry lacks autonomous, intelligent systems capable of self-governing both operational efficiency and environmental accountability in real time. This work presents SAGE (Sustainable Agentic Governance Engine), a novel dual-agentic AI framework in which two purpose-built autonomous agents operating with goal-directed reasoning, environmental perception, adaptive decision-making, and inter-agent coordination collaboratively govern the entire LLM deployment lifecycle. The first agent, the Optimization Agent, functions as an autonomous orchestrator that continuously perceives pipeline states, reasons over resource utilization patterns, and executes self-optimizing actions for pipeline tuning, model serving configurations, dynamic resource allocation, and cost reduction through a closed-loop feedback mechanism eliminating human-in-theloop bottlenecks and enabling proactive, rather than reactive, operational governance. The second agent, the Green AI Agent, operates as an autonomous environmental auditor for LLMs that independently instruments, collects, and evaluates computational efficiency indicators including FLOPs, energy consumption (kWh), latency at P50/P95, throughput, inference speed, and CPU/GPU/RAM utilization alongside carbon footprint (CO2. emissions) externalities, autonomously mapping these metrics against SDGs 7, 9, and 13 through standardized sustainability scoring. Critically, SAGE agentic architecture enables both agents to communicate, share contextual state, and trigger cross-agent optimization loops whereby the benchmarking agent's sustainability assessments directly inform and constrain the Optimization Agent's resource allocation decisions, creating an emergent, co-adaptive governance system that neither agent could achieve in isolation. By grounding LLMOps in agentic AI principles of autonomy, reactivity, proactivity, and social coordination, SAGE transforms sustainability from a post-hoc audit concern into an embedded, agent-driven, real-time governance mechanism, reframing LLM operations as a socio-technical responsibility aligned with global climate commitments, a convergence of agentic AI, sustainable computing, and responsible AI that remains significantly underexplored in current academic and industrial research. The framework provides a reproducible, scalable pipeline for the responsible deployment of LLMs in realworld, resource-constrained edge environments. The pitch can be found here: https://fatimarani.github.io/SAGE/