Objectives: The objectives of the current study are twofold. First, it aimed to explore the prevalence of depression, anxiety and stress symptoms (i.e., psychological disorders) among Kuwait University students. Second, it sought to identify and quantify the associated risk factors as well as the students’ coping strategies utilized to address these psychological disorders. Methods: We used a cross-sectional study at Kuwait University and selected students using a multistage stratified cluster sampling design among the 15 faculties of Kuwait University. To serve the study purposes, two cross-cultural and validated instruments were used, including the Depression, Anxiety and Stress Scale 21 (DASS-21) and the Brief-COPE scale. Descriptive statistics, as well as logistic regression analysis, were used to analyze the study findings. Results: A sample of 1142 students from various faculties participated in this study. We found that 681 (59.6%), 791 (69.3%) and 588 (51.5%) of the participants had depression, anxiety and stress symptoms, respectively. The highest coping strategies for stressors and challenges faced were moderate and high emotion-based coping strategies (n = 1063, 93.1%). Students from the Faculty of Allied Health Sciences as well as students from the Faculty of Engineering had significantly higher stress levels compared with students from other faculties (p < 0.05). Our results demonstrated that family problems were consistently a significant predictor of depression, anxiety and stress symptoms among Kuwait University students (p < 0.05). We further found that students who presented with stress and anxiety symptoms and those who practiced avoidant-focused coping strategies were substantially more likely to experience depression (ORs ≥ 2.7, p < 0.01). Conclusions: Our findings inferred that the majority of Kuwait University students have a remarkably high prevalence of mental health problems, mainly anxiety, depression, and stress symptoms along with inconsistent coping strategies toward the faced challenges during their studies. Therefore, the most important recommendation of the current study is the establishment of counselling centers in all faculties at Kuwait University. In turn, doing so facilitates the integration of wellness programs and the provision of comprehensive educational seminars, specialized training sessions and self-management techniques for Kuwait University students, leading to desired academic outcomes.