During the past two centuries, universities have evolved from being “accumulators” of knowledge, largely separated from society, to “knowledge hubs,” which are deeply embedded in systems of innovation and take on the role of instigating economic and social development. Despite economic, social, and institutional disparities, university authorities, policymakers, and academics are focusing their attention on the potential of universities to create innovative environments and contribute to the knowledge-based economic development of countries and regions. Due to the lack of data, almost all extant empirical studies have analyzed the contribution of university research mission on developed regions (e.g., USA, UK, and the Netherlands). The aim of this paper is to provide evidence of the impact of three university missions on the economic development of countries at different stages, namely the factor-, efficiency-, and innovation-driven stages. Adopting the endogenous growth theory, our proposed model was tested using data from 77 countries with a linear regression model. Our main results show that: (i) the human capital generated by universities is the most important predictor of economic development at all stages; (ii) the university research activity is only evidenced at the efficiency-driven and innovation-driven stages; and (ii) the outcome of the entrepreneurial mission of universities is only positively related to gross domestic product (GDP) in innovation-driven economies. Some relevant implications for policymakers, university managers, and society, as well as best practices emerge from this research.