The literature in the field identified over time a series of economic and non-economic factors that trigger the process of economic growth and convergence. Despite the fact that most of the theoretical as well as the empirical studies address the determinants of the economic growth process only from an economic perspective, a series of recent debates draw the attention upon a neglected category of factors until now, namely the quality of the economic growth process and the role of institutions as important tools in promoting convergence/divergence between economies. This new area of research, named institutional economics, highlights the role of institutions in protecting the property rights and the contracts (Han, X., et all 2014). Although these factors were often ignored as explicative variables of the economic growth process, in comparison to factors such as human capital, physical capital or technological progress, recently economists, researches or other participants in the market became highly aware of their importance. The primary objective of the current paper is to analyze the concept of economic governance as detailed within a series of studies in the field, or as perceived by international organizations. In addition to this objective we present some main indicators used to measure the quality and efficiency of the economic governance process with precise data and evolutions for the member states of the European Union. The main conclusions of our study reveal the fact that in order to achieve high levels of economic growth and convergence across European Union member states there is a strong need for enforcing the legal framework of EU along with the transfer of the power regarding the development, management and implementation of the economic stability policies from the national to the supra-national level. Also a harmonization of the institutional structure is required as a measure for supporting economic performance.