The article substantiates the need for the formation of the intellectual and pedagogical competence of postgraduates of future university teachers in the conditions of a sustainable innovative educational environment. The essential characteristic of intellectual and pedagogical competence, its components, including the ability to apply the acquired knowledge for the effective implementation of the process of teaching and upbringing of students, the ability to innovative pedagogical activity are revealed. The relevance of the problem of the formation of this competence at the scientific and pedagogical level is due to the need to select the content of educational disciplines of the pedagogical cycle, based on the requirements of the professional activity of a teacher, a teacher-researcher with a focus to new social demands, that determine the goals of sustainable development of higher education. In a professionally oriented aspect, the formation of the intellectual and pedagogical competence of postgraduates is directly dependent on the ability to implement educational programs, to apply modern technologies and methods of teaching and educating students, on the readiness for pedagogical activity as a teacher, teacher-researcher, which entails the need to master intellectual and pedagogical knowledge and skills, projected on the solution of professional tasks, that constantly arise in the educational process.