Embedding sustainability and green thinking throughout higher education is decisive to preparing future professionals to address the pressing environmental, social, and economic challenges of our time. Universities play a pivotal role in this transformation, acting as catalysts for the transition towards a sustainable and resilient global society. By integrating sustainability competences into curricula, higher education institutions foster systemic thinking, innovation, ethical leadership, and collaboration, essential capacities for shaping a just and green future. The European Commission’s Joint Research Centre (JRC) developed GreenComp: The European Sustainability Competence Framework, as a common reference to promote learning for environmental sustainability across all educational levels, with an invitation to deploy it at different education al levels. GreenComp defines twelve competences organised into four interconnected areas (embodying sustainability values, embracing complexity, envisioning sustainable futures, and acting for sustainability), providing a holistic foundation for sustainability education. Building upon this foundation, the GREENVERSITY Project (2024-1-ES01-KA220-HED-000257362) has adapted and expanded the GreenComp principles to the specific context of higher education through the development of the GREENVERSITYCORE Framework of Sustainability Competences in Higher Education, which is the main core of this report. The GREENVERSITY CORE organises each competence area into detailed components of knowledge, skills, and attitudes (KSA), following a taxonomy that enhances conceptual clarity and applicability. To support effective implementation, a three-level rubric has been developed for each KSA dimension, guiding educators in assessing the progressive acquisition of competences and facilitating alignment with course learning outcomes. This structured and evidence-based approach ensures coherence, transparency, and adaptability across diverse disciplinary and institutional contexts. The GREENVERSITYCORE Framework offers distinct advantages for all its target beneficiaries. For educators, it provides clear guidance and practical tools, such as KSAs and rubrics, to integrate and assess sustainability competences across disciplines with ease and consistency. Students benefit from a more holistic and transformative learning experience that builds their capacity for systemic thinking, critical reflection, and responsible action. Universities and institutional leaders gain a coherent model for embedding sustainability within curricula and accreditation systems, enhancing quality, visibility, and societal impact. Finally, policy makers and accreditation bodies can rely on the framework as a standardised, evidence-based reference to promote alignment, comparability, and progress toward European sustainability education goals.