The measurement of inequality and its determinants are major tasks within the economic literature. The main objectives of this paper are to identify patterns of convergence in the income inequality in European Union countries and to investigate the factors behind the formation of convergence clubs. For those purposes and considering the Gini index during the period 2007–2018, the club convergence approach and an ordered logit model are employed. The results show four clubs and four divergent countries. In addition, the analysis identifies certain factors, such as economic openness, public intervention and education, as the main drivers of inequality reduction. Finally, the results from the club convergence analysis for an alternative inequality measure, specifically the ratio 80:20, are similar to those achieved in the case of the Gini index.