Entrepreneurship is becoming understood as a set of competencies needed for many professions and, as a result, requires to be integrated into higher education even in such seemingly distant areas as, e.g., public administration, sport, agriculture, tourism, etc. Therefore, there is a need for research-based guidance on how to introduce and develop entrepreneurial education as an enabling approach to the transition in higher education that could serve as an integral part of a paradigm shift towards an entrepreneurial university. This paper aims to support that transition and to address related challenges by the presentation of a new progression model, which provides guidelines for the development of courses at the tertiary level with an entrepreneurial university approach. The construction of the new applicable model is central to the purpose of this study and based on a systematized literature review. Additionally, the input–process–output–outcome framework, originally constructed for the evaluation of educational programs, was adapted to the incorporation of an overall framework into the new model. In the results, the paper redefines some of the relevant core terms, such as “entrepreneurial education” and its “progression model”. The research outcomes offer broad practical and theoretical applicability to a range of stakeholders—educators, students/learners, industry/business, policy makers, and researchers.