As artificial intelligence evolves beyond passive tools into autonomous agents, higher education institutions (HEIs) stand at the edge of a new paradigm: Agentic AI. This perspective paper explores the transformative potential of this nascent, yet powerful, class of AI systems capable of autonomous decision-making, goal pursuit, and contextual adaptation. This paper contrasts Agentic AI with Generative AI, clarifying the critical distinction often missed in public discourse. The paper outlines five strategic opportunities that Agentic AI offers to HEIs, from redefining strategic planning and policy-making to transforming teaching, learning, scientific research, and administrative operations. Then, it examines institutional challenges to adoption, including ethical ambiguity, trust deficits, infrastructural limitations, and resistance to change. After that, the paper proposes practical, value-driven strategic pathways to achieve responsible, successful Agentic AI adoption. This paper aims beyond information to guide HEI leaders, technologists, faculty, and researchers in navigating the complex landscape of Agentic AI by providing conceptual clarity, strategic insights, and a call for interdisciplinary collaboration in transforming higher education.