The European Commission has given special attention to the digital evolution of the European economy and society since the early 2000s. Starting with 2014, the Digital Economy and Society Index has become a key monitoring and assessment instrument. In 2021, the main indicators of the Digital Economy and Society Index were matched with the Digital Agenda 2030 targets, which encompass four dimensions: human capital, connectivity, digital technology integration, and digital public services. The article aims to verify the convergence amongst Member States in integrating digital technologies, which is the third dimension of the Digital Economy and Society Index yearly database. The σ-convergence analysis assessed decreased disparities in digital technology integration between Member States over time. The β-convergence analysis was used to evaluate the pace of catch-up from the initial development level. The σ-and β-convergence were not confirmed. The specific digital technology integration indicators (11) are studied to identify crucial areas that must be addressed in the future to guarantee that digital inclusion is as widespread as feasible. The present research is concentrated on the member countries that joined the EU during the Eastern enlargements. All individual indicator performance is typically behind the EU average, and as the β-convergence study indicates, the average catch-up rate is not encouraging.