The integration of Green Artificial Intelligence (AI) technologies into educational systems offers a promising avenue to enhance operational efficiency while addressing sustainability challenges. Through a rigorous three-phase methodology combining literature review, AI agent development, and participatory workshop-based case analysis, this paper highlights the pivotal role of AI agents, as applications of Green AI technologies, in driving transformative outcomes within schools. By directly improving self-learning efficiency and reducing learning costs for students, enhancing management and service efficiency, reducing labor costs for schools, as well as minimizing resource dependence for both teachers and students, AI agents create a foundation for sustainable operations. These direct effects generate positive spillover effects, cascading into broader outcomes, including innovation performance, economic efficiency, and environmental sustainability, aligning with the United Nations Sustainable Development Goals (SDGs). By presenting a comprehensive conceptual model, this study demonstrates the pathways through which Green AI contributes to sustainable development in education and emphasizes its critical role in bridging technological innovation with sustainability. This framework provides significant theoretical insights for further empirical research while offering actionable strategies for policymakers and educators to harness Green AI for building sustainable schools with a student-centered approach.