The aim of the paper is to define the current state, possibilities, and prospects of digitalization of the Russian system of (higher) education while maintaining the current approach to state regulation of this process and developing a new (improved) approach for its acceleration. For this purpose, a method for estimating the degree of digitization of the (higher) education system has been developed and applied. As a result, it is found that at the present time (2018), the greatest degree of digitalization is characteristic for additional indicators of the functioning of the system of (higher) education in contemporary Russia, such as the work of library resources and state and public monitoring. At the same time, the degree of digitalization of key indicators (educational and research activities of universities) is low. At the same time, the infrastructure for digitalization of the Russian system of (higher) education is sufficiently developed, which determines significant opportunities for the further development of this process. The final degree of digitization of the Russian system of (higher) education is estimated at 25.8% and is very low. The reason for this problem lies in the inadequate state regulation of the process of digitalization of the Russian system of (higher) education. To solve the problem, the authors developed and presented a new (improved) approach to state regulation of the digitalization of the Russian system of (higher) education. This approach implies full-scale financing of relevant activities, priority promotion of digitalizing the main activities of the (higher) education system, as well as orientation to the proposed model for the functioning and development of a (higher) education system based on digital technologies. Its practical implementation will increase the efficiency and competitiveness of the Russian system of (higher) education.