In this article the authors are substantiation the significance of the universal competence of intercultural interaction by means of the fine arts in the formation of the personality of students of the university. They are proving the urgency of the problem of this study. This problem is due to the versatility of the phenomenon of culture and art and the potential of its influence on the diverse spheres life of human. The development of intercultural interaction of students by means of the fine arts actively influences the self-determination of their personality. This allows students on the basis of cultural, spiritual, moral values to impose responsibility on themselves in decision-making in all spheres of life. This allows students to lay responsibility on themselves in making decisions in all spheres of life based on cultural, spiritual, moral values. Peculiarities of international cultures as a phenomenon of intercultural interaction are revealed through the fine arts, through artistic images. Theoretical research of intercultural interaction showed the lack of knowledge of the scientific and theoretical foundations of intercultural interaction as a universal competence by resources of fine arts. A chain of interrelated categories of intercultural interaction of the students' personality by means of the fine arts are determining by the authors of this article. The theoretical and experimental studies that were carried out convincingly prove the need for further to development and introduce into the educational process an innovative model of forming the universal competence of intercultural interaction of students of the university by resources of visual arts.