The aim of this article is to indicate the rationale for the development of the bioeconomy in selected EU countries depending on their overall level of economic development. The research was based on four highly developed countries, i.e., Germany, France, Finland and Denmark, and four medium-developed countries, i.e., Poland, Hungary, Czech Republic, and Slovakia for the period 2001–2018. Renewable energy consumption, biomass and agricultural production were analysed as determinants of the bioeconomy development. The question was also answered whether differences in terms of measures determining the level of bioeconomy development between countries with different levels of economic development during the studied period are decreasing or increasing, using sigma (σ)-convergence coefficients. It is shown that the development of the bioeconomy of the studied countries is related to their level of economic development. In the middle economically developed countries, real opportunities for the development of the bioeconomy are noted, through a high share of agriculture in national income; and in highly developed countries—high spending on research and development and the growth of eco-innovation, which contributes to maintaining a development advantage between these groups of countries.