The subject of this research is the international competitiveness of post-Soviet national economies, within the framework of a new integration association in the post-Soviet space – the Eurasian Economic Union (EAEU). In the context of studying the competitiveness of the member-states of international regional integration associations, the authors analyze and conditionally divide the scientific and theoretical reserve of Russian and foreign scholars into several key vectors of research. The article formulates the approaches towards assessing the impact of integration processes upon the competitiveness of national economies of the EAEU member-states. For the analysis of competitiveness of the participant countries in the integration alliance, the authors applied the methodology of the Global Competitiveness Index of the World Economic Forum. The competitiveness of participant countries of the alliance was examined in accordance with the eight main criteria: the effectiveness of state institutions, infrastructure, the level of macroeconomic stability, development of financial markets, effectiveness of goods and services market, effectiveness of the job market, development of human capital, and assessment of innovation activity. The conclusion is made that all the countries participating in post-Soviet integration association indicate positive dynamics in their international competitiveness, although its level differs considerably. The approach towards assessing the impact of integration upon the competitiveness is formulated. It is noted that the achievement of higher level of competitiveness is impeded by macroeconomic instability of the national economies of post-Soviet space. Recommendations are given in the formation of their competitive advantages within the framework of the integration union.