Technological entrepreneurship is one of the mechanisms for creating a regional innovation system, which is especially important for the Russian Far East. In modern conditions, the most productive formation of regional innovation systems takes place within the framework of the triple helix model. Higher education institutions are a key element; they are seen as centers of innovation and regional development, ensuring integration of educational, research and entrepreneurial activities. The innovative vector of development imposes special requirements on formation of technological skills and specific economic knowledge. All actors of the triple helix model, i.e., the state, business, higher education institutions participate in forming technological entrepreneurship competence. However, the large number of research and development projects created at universities contrasts sharply with the small number of inventions brought to commercial use. The difficulties that arise in this sphere are manifested to a greater extent during commercialization of scientific and technical developments. The goal of the study is to develop proposals for forming technological entrepreneurship competences in higher education institutions. We have found that the dominant role in the interaction of actors in the triple helix model belongs to the entrepreneurial university as a key element in forming relevant knowledge and skills. We have established that forming technological entrepreneurship competences becomes synchronized with research and educational activities. Based on expert estimates, we have substantiated the professional competences required for innovative entrepreneurs for planning, creating and developing high-tech businesses. We have offered a mechanism for forming competences of technological entrepreneurship that is best adapted to conditions of the local university. We have developed and substantiated specific proposals for forming competences, including consistent implementation of the optional interdisciplinary module "Entrepreneurship" in the educational process. It is proposed to create a "project office" as part of the educational and methodological management of the university. The results of the study and the recommendations developed on their basis can be used in practice for forming technological entrepreneurship competences in higher education institutions.