The increase in studies on how digital transformation based on the application of digital technologies affects the sustainable development of various sectors of the economy has been observed. Although digital transformation is important for the financial sector sustainable development, the drivers and links between them are weakly addressed by researchers. The study is aimed at exploring how digital transformation due to the application of innovative technologies and solutions, especially digital payments, is leading to the financial sector sustainable development through financial inclusion and operational efficiency. The current research presents the study of the financial sector digital transformation and its sustainable development based on a systematic literature review, a secondary data analysis, and expert interviews to provide further research directions and draw practical suggestions for professionals on the financial sector digital transformation toward sustainable development in the future. A systematic literature analysis is performed based on text analytics, a bibliometric analysis, and network maps aimed at acknowledging the existing research outcomes and identifying the research gaps on the digital transformation agenda in the financial sector. The collected data on the digital payments’ dynamic in the EU were analyzed with the use of statistical methods, including a correlation and regression analysis. Structured expert interviews were used to validate research findings and to highlight key issues of the digital transformation in the financial sector of Baltic countries. The authors have paid special attention to the sustainable development of the financial sector’s economic dimension and its efficiency indicators, such as financial inclusion and digital payments’ intensity. A social dimension is limited toward financial inclusion based on digital payments’ offering. The research results indicated recent trends in digital transformation and types of usage of digital technologies in the EU and Baltic countries to ensure the sustainable development of financial institutions. Furthermore, the results revealed a significant increase in the digital payments’ intensity during the last years in the EU, as well as a close relationship between digital payments with financial inclusion and operational efficiency of financial institutions.