The study aims to disclose the role of the universities and students' backgrounds in predicting student engagement. The study uses Monitoring of Education Markets and Organizations (MEMO) of 2015 and 2017, which is hierarchical nationally representative data set of 5,251 undergraduate students nested into 135 universities in Russia. Four indices were developed to measure student engagement based on behavioural approach, namely, class engagement, learning engagement, research engagement, and extracurricular engagement. The mixed-effects multilevel modelling was used to test the hypotheses on university roles and students' background characteristics. Students' parental family characteristics did not appear to have a strong influence on student engagement except mothers' higher education. High school achievements are very important for further student engagement. The findings highlight the importance of motivation and career ambitions of students. Plans to work within the field of study or to pursue further studies to obtain a MA or Ph.D. degree positively associated with student engagement. The results confirmed that the academic environment is the strongest predictor of student engagement. Universities need to develop active teaching practices to improve the academic environment and increase student engagement.