Our paper investigates key tools of developing students' leadership at higher educational institution for their successful adaptation in the labor market. The key problems facing the youth labor market today are: a high rate of real youth unemployment, the problem of neet-youth, discrimination in the labor market on the ground of age, etc. The article substantiates the urgency of studying the phenomenon of leadership, highlighting the most important leadership qualities and searching for ways of their formation and further development in young people. It also gives a brief description of leadership as a social phenomenon, provides basic approaches to leadership, and highlights key qualities of today's leaders. The paper presents summarized results of a survey conducted among modern international higher educational institution students on the necessary qualities of a leader among students of a modern international university, during which there were named the following key qualities (self-confidence, independent character, public-speaking abilities, riskiness, sense of humor) and the least important from students' point of view (tact, adaptability, insight into human nature, and sympathy). It also emphasises the main methods of developing young people's leadership, among which we should mention: creative and project activities, trainings and master classes on leadership, meetings with experts, self-management, special courses in leadership within educational programs, competitions, participation in R&D, extracurricular activities, leadership schools. We place particular emphasis on the importance of comprehensive approach to the development of leadership qualities of students at modern institutions of higher professional education, covering all tools for developing leadership skills.