Purpose: The purpose of the article is to determine the contribution of the EAEU into growth of the global GDP and to develop recommendations for using the potential of the processes of regional integration in their becoming the basis of acceleration of growth and development in the global economy. Methodology: The contribution of the processes of regional integration in accelerating the rate of growth and development of the modern global economy is studied with the help of the method of regression analysis in three consecutive stages. The first stage includes determination of regression dependence of growth rate of the global GDP on aggregate GDP of the NAFTA countries in 1994–2018 (after creation of the regional integration union). The second stage includes determination of regression dependence of growth rate of the global GDP on aggregate GDP of the EAEU countries in 2007–2014 (before the creation of the EAEU; at the third stage—in 2015–2022 (after creation of the EAEU, the data for 2019–2022 are the forecast data). The information and analytical basis of the research is statistical materials of the International Monetary Fund. Results: Emergence of synergetic effect during creation of the EAEU is observed—it is connected to provision of its substantial and sustainable contribution into acceleration of the growth rate of global GDP as compared to NAFTA, which contribution is negative and not significant statistically. Recommendations: It is shown by the example of the EAEU that this contribution is predetermined by the specifics of integration within a regional union of countries. Apart from traditional increase of the volume of foreign trade (due to elimination of internal customs barriers and entering the world markets), active and highly-efficient cooperation in the sphere of R&D, marketing, and investments is conducted. Development of this cooperation is recommended as a perspective measure of provision of contribution of other modern regional integration processes in acceleration of the rate of growth and development of the global economy.