PURPOSE: From the perspective of positive psychology, and based on Self-Determination Theory and Sustainable Happiness Theory, this study explores the relationship between basic psychological needs and psychological well-being among undergraduate students, as well as the mediating roles of autonomous motivation and academic engagement. METHODS: A survey was conducted among 439 undergraduate students using the Basic Psychological Needs Scale, Learning Motivation Scale, Academic Engagement Scale, and Psychological Well-being Scale. RESULTS: Basic psychological needs were significantly and positively correlated with undergraduate students' psychological well-being. Academic engagement partially mediated the relationship between basic psychological needs and psychological well-being. However, autonomous motivation did not mediate this relationship. Furthermore, autonomous motivation and academic engagement served as chain mediators in the relationship between basic psychological needs and psychological well-being. CONCLUSION: Basic psychological needs are not only directly related to undergraduate students' psychological well-being but are also indirectly associated with their psychological well-being through the mediating role of academic engagement and the chain mediating role of autonomous motivation and academic engagement.