The main objective of the paper is to present the development of digital economy and society in the Countries of the European Union in the light of the digital convergence of these markets. The analysis was based on the data on the Digital Economy and Society Index (DESI) from 2015 and 2020. Empirical studies have been conducted in two stages. First, basic measures of time series dynamics were used to determine the dynamics of changes in index values. On the other hand, in order to classify countries in terms of similarity of value and structure of the DESI, a cluster analysis was used as one of the basic methods of the so-called unsupervised statistical grouping. The studies presented confirm that the levels of indicators and the dynamics of changes in their value at the level of the synthetic DESI indicator, and in the five underlying areas of analysis, vary despite the fact that almost all are pro-growth, including for isolated clusters of EU-28 countries. When analyzing the DESI synthetic index and its components, it was concluded that there is generally an increase in convergence between the EU-28 countries in terms of the level of development of the digital economy and society, as well as in four components: Connectivity, Human Capital, Use of Internet Services and Digital Public Services. The Integration of Digital Technology area was the only one where increasing polarization of results was observed. The added value of the paper is to fill the research gap in research on the digital convergence of markets in the Countries of the European Union.