The article analyzes the experience of public and private-based governance of EU universities, which occupy leading positions in The Academic Ranking of World Universities (ARWU) (L'Université Paris-Saclay, Ludwig-Maximilians-Universität München, Oxford University, Sorbonne University, Stockholm University, The Karolinska Institutet, TUM, University of Cambridge, University of Oxford, University of Warsaw). The significance of the deepening of public and private-based university governance in the strategic priorities of the studied institutions is analyzed. It was determined that the strategic goal of the development of private-based university governance is to deepen the innovative culture of universities; to create of a world-class regional innovation ecosystem; to grow influence of universities at the regional, national and global levels; to build constructive relations with local and regional communities; to encourage the wide use of research results. Based on the understanding of experience and best practices, the models of public and private-based university governance are substantiated - the model of public engagement, the model of academic partnerships, the model of institutionalized public and private-based university governance, the model of multi-level public and private-based university governance. The functional peculiarities and legal support of the functioning of institutions of public and private-based university governance in the studied universities are presented - the Council of the University of Stockholm, the Council of the University of Warsaw, the University Council and the Advisory Council of the Ludwig-Maximilians-Universität München, the Advisory Council of the University of the TUM, the Supervisory Council and the Council of the Technical University of Munich, the Board of Directors of L'Université Paris-Saclay, Board of Directors of Sorbonne University). The architecture of the multi-level public and private-based governance system of the United Kingdom Research and Innovationorganization is analyzed. It was concluded that this model promotes transparency, accountability, efficiency, ensures the development and implementation of the institution's strategy, the accountability of its officials, the leadership and responsibility of each structural unit, allows to implement result-basted activities, promotes industry representation and diversification of activities, provides a wide coverage and involvement in the process of governance representatives of various stakeholders – professional communities, state and local self-government bodies, charitable and public organizations, opinion makers, trade unions.