Real convergence has been considered a fundamental pillar of the European Union and has become more and more debated with the accession of the countries from Central and Eastern Europe to the European group. The main purpose of this paper is to study the economic growth and the real convergence within the enlarged European Union. Moreover, we have tried to analyze the social dimension of the convergence by including in the study three indicators of the labor market: employment rate of young people, compensation of employees and tertiary education attainment. In order to analyze the process of real convergence, we have calculated the coefficient of variation taking into consideration two main clusters of countries: The Old Member States and the New Member States. Our study suggests that the Community's economic landscape continues to be dominated by significant gaps between countries. As far as the well-being of the European citizens is concerned, our study suggests that within the New Member States cluster, the gaps have constantly diminished starting with 2004. In contrast, in the Old Member State group, the economic divergences have been accompanied by discrepancies in the labor market. Although there were voices that argued that the enlargement of the European Union would undermine its economic and political power, it seems that the New Member States group is making important progress in terms of economic convergence, also enhancing the well-being of its citizens.