The new approach to the higher education modernization based on the realization of competency-building modular programs has been considered. This approach closely supports competency-building approach to professional training of modern specialists within the context of current theoretical and methodological principles. The European dimension of competency-building approach and its basic concepts as well as its implementations in educational process have been characterized. It has been stressed that competency-building approach shifts the focus from teaching to acquiring competencies within the educational process. It has been defined that labor market growing demands, rapid technological change, globalization, increased academic and labor mobility require the use of the competency-building approach to future teachers' aptitude to improve their professional level, which is a pre-requisite and priority in higher pedagogical education modernization. The connection of the competency-building approach with individually-oriented and active approach to learning has been considered, as it concerns student's individuality and can be implemented and tested only when an individual student carries out a certain set of actions. The approach requires the transformation of the educational content, its conversion from the objective model that exists for "all" the students, to subjective outcomes of each student, which can be measured.