Focus on the quality of education is a priority of the state program of the Russian Federation “Development of education” (approved by the RF government decree of December 26, 2017 № 1642). The main activities of the direction “Improving the management of the education system” of this program include measures to implement mechanisms for evaluating and ensuring the quality of education in accordance with state educational standards. Assessment of the quality of education in the universities is determined by the necessity of the competence orientation of the educational process and its content, technology implementation, re-evaluation procedures, technologies and tools to assess the quality of training students within the framework of the competence-oriented educational standards. The article deals with the problem of evaluating the quality of training of students of higher educational institutions. The definition of the concept of quality of education from the point of view of stakeholders is given.  The article presents a method for evaluating the formation of learning outcomes based on a two-criteria approach (competence and disciplinary). The main criteria for evaluating the formation of learning outcomes are highlighted. The results of testing the methodology in one of the areas of training are considered. To study the level of competence formation, a scale of assessment of competence formation (the stage of competence formation) is proposed. The results of testing the methodology for evaluating the formed learning results presented in the article can be useful for interested persons who are directly involved in the process of designing, developing and implementing educational programs, as well as in making methodological and managerial decisions aimed at improving the quality of education.