The presented article considers the result of the flexible software development methodology - Agile - implementation into the process of higher education students teaching. We present approaches to the educational process modernization, educational and methodological support development and approaches to teaching in high school on the example of the discipline "Algorithmization and basics of programming" for students in specialty 122 Computer Science in educational program "Applied Programming". Authors analyzed a wide range of publications outlining the issues of developing new teaching methodologies, including the problems of training future IT-specialists in the information society transformation realities and the educational process informatization. The analysis of the information technologies market and inquiries of the leading companies in the market of Ukraine is carried out, besides that the reflections of graduates concerning efficiency of training in modern higher education establishments are investigated. The article describes the results of several years gradual adaptation of Agile technology to the learning process, its introduction into the learning process and the results of the developed methodology approbation. The theoretical bases and advantages of Agile-methodology over the classical scheme of training, which we define as "direct" or "cascade", are considered. In order to effectively study the impact of flexible methodologies on the educational process, approaches to the formation of experimental and control academic students' groups are presented. The dynamics of laboratory work timeliness and comparison of the academic groups' final results are given. The influence of Agile-methodology on the academic groups success is considered and a statistical comparison with the classical approach to teaching is made. Also, we determined the directions of further research on the topic of Agile-methodology implementation in the educational process taking into account the urgency of the education transformation issue in Ukraine and professional training of specialists in the field of information technology.