The relevance of this article is due to the need to form and develop algorithmic thinking of higher education students as the main requirement of the information society following 21st century skills and competences for new millennium learners. The purpose of the article is to consider algorithmic thinking as a new dimension of learning in higher education. The leading approach to the study of this problem is the analysis of methodological literature, and the experience of students, teachers, and academic staff. The article considers the essence, main properties, and characteristics of algorithmic thinking, suggests the universal sequence of algorithm development and model of algorithmic thinking as well as determines its importance for any subjects outside the information and communications technology area. The materials of the article can be useful for lecturers, professors, and other academic staff of universities and institutes when studying any subjects related to the basic and professional training of students.