To study STEM and STEAM education as an innovative technology, the authors of the paper conducted a comprehensive theoretical and methodological study on the stated problem. A comprehensive theoretical and methodological study was directed towards the solution to the problem of developing a new model for the STEM and STEAM education system to make correct management decisions in the framework of the country’s socio-economic development based on objective data. The object of the study was STEM and STEAM education as an innovative technology. The subject of this study is the mechanisms of STEM and STEAM-education in the system of higher professional education of the Russian Federation. The methodological foundation of the study was the general scientific ideas for holistic, systemic, and integrative approaches to the study, which gave an opportunity to assess a set of interrelated and interacting elements that form a certain integrity. The use of these approaches provided a comprehensive analysis and formulation of the research problem and determined the strategy for its study. Both theoretical and empirical methods of studying the indicated problem were used in the comprehensive theoretical and methodological study presented in the paper. The leading methods of scientific knowledge were the following: the method of comparison; phenomenological data analysis; discourse analysis of the text; theoretical analysis; empirical description (expert assessment method and in-depth interviews). The result of the study is the STEM education model developed by the authors as an innovative technology in the system of higher professional education of the Russian Federation. The materials of the paper will be useful for specialists in the field of higher professional education, teachers of natural sciences and humanities, the teaching method of which is based on the STEM approach.