Students, as a relatively health-informed population group, may still have limitations in health literacy, which is a concern as students take increasing responsibility for their health and make independent health decisions. The aim of this study was to evaluate the overall attitudes towards COVID vaccination among university students and to investigate various factors contributing to vaccination willingness among health and non-health studies students. A total of 752 students from the University of Split were included in this cross-sectional study and completed a questionnaire that consisted of three sections: socio-demographic data, health status information, and information on vaccination against COVID-19. Results show that the majority of students of health and natural sciences were willing to be vaccinated, but the majority of students of social sciences were not (p < 0.001). Students who used credible sources of information had a more significant proportion of those willing to be vaccinated and the majority of students who used less credible sources (79%) or did not think about it (68.8%) were unwilling to be vaccinated (p < 0.001). Multiple binary logistic regression modeling shows that female gender, younger age, studying social sciences, negative opinion about the need to reintroduce lockdown and the effectiveness of epidemiological measures, and usage of less credible sources of information were the most important factors contributing to increased vaccination hesitancy. Therefore, improving health literacy and restoring trust in relevant institutions can be critical in health promotion and COVID-19 prevention.