Influence of internationalization of higher education on its quality was concerned in the article and also the competence of the subjects of public administration in the institutionalization of the relevant process were justified. The article contains the results of analysis of the content of separate state and university programs on involvement of the most trained foreign students to study at the institutions of higher education, which are used in the systems of higher education in China, Romania, Hungary and Turkmenistan. Were made conclusions concerning approaches to improve the mechanisms of higher education with the help of regulating norms on the amount of foreign students and teachers in the framework of the structure of the institution of higher education , as well as the need to introduce scholarships and financial incentives by public authorities and the administration of the institution of higher education to attract foreign citizens to study.