The article covers a number of issues related to the problem of the specialist-professional formation in the system of higher education of Ukraine, taking into account global challenges and prospects for the development of the world economy, national economies and modern society. In the process of scientific research, an understanding of the basic concepts of «profession», «vocational training», «formation of a specialist-professional», «IHE activity» has been formed. The role and significance of higher education in professional training of specialists, competitive in the labour market are revealed; the priority directions of development of the industry are singled out in accordance with the state educational policy requirements and the Bologna process tasks in the conditions of the European Higher Education Area formation and the integration implementation. The article pays particular attention to analysing the models of national strategies for the higher education development and selecting the model of the Ukrainian universities development strategy on the path to their promotion to world rankings, referring to the experience of autonomy, mission, results of activity and achievements of European and world universities. Consequently the research analyses of the educational institutions network during the years of Ukraine's independence, taking into account external destabilizing factors; gives the characteristic of the local IHEs’ activity, including universities, during the period of reforming and modernizing the higher education system according to European standards and time requirements; determines the new approaches and directions of the IHE's activity improvement in the field of training qualified specialists for the industrial and social spheres. Moreover the article reveals the features of key trends for the modern education sphere, among them there is a globalization, the factor of ICT, the growth of non-system education, individualization and personalization of educational trajectories. It also gives the characteristic features of a competitive specialist-professional who is able to function effectively in the modern labour market. The benefits of this study are: the defined forms of the educational process organization at IHE in accordance with the Law of Ukraine «On Higher Education»; the given classification of innovative teaching methods for realizing of the educational process participants’ abilities and talents, basing on the study of scientific and methodological literature; the determined new approaches and directions of the IHE's activity improvement in relation to the training of qualified specialists for the industrial and social spheres. On this basis, the training of competent specialist-professionals should be considered as one of the priority areas of scientific research with the definition of long-term educational strategies, including goals, tasks, scientific approaches, positions, directions and ways of their implementation in the higher education system. In the search process, the methods of theoretical research and practical implementation of this problem are used, in particular: analysis and generalization of scientific approaches and ways for improving the professionals formation process in the higher education system; international experience synthesis and comparison, normative legal acts and peculiarities of the IHE work in the professional staff training; induction and deduction when disclosing forms and methods of future specialists’ educational activity, gaining their professional qualities and characteristics.