Towards the transition to blended and remote education, evaluating the levels of students' digital competence and designing educational programs to advance them is of paramount importance. Existing validated digital competence scales usually ignore either important digital skills needed or new socio-technological innovations. This study proposes and validates a comprehensive digital competence scale for students in higher education. The suggested instrument includes skills of online learning and collaboration, social media, smart and mobile devices, safety, and data protection. The scale was evaluated on a sample of 156 undergraduate and postgraduate students just before and at the beginning of the COVID-19 crisis. The final scale is composed of 28 items and six digital competence components. The evaluation study revealed valid results in terms of model fit criteria, factor loadings, internal validity, and reliability. Individual factors like the students' field of study, computer experience and age revealed significant associations to the scale components, while gender revealed no significant differences. The suggested scale can be useful to the design of new actions and policies towards remote education and the digital skills' development of adult learners.