Artificial intelligence (AI) technologies have profoundly influenced both professional environments and personal lives. In the rapidly developing sector of AI education, fostering essential AI literacy among university students has become vital. Nevertheless, the factors that determine AI literacy remain insufficiently defined. This research, grounded in self-determination theory (SDT), seeks to investigate the relationships among three components: the fulfillment of university students’ three psychological needs, self-regulated learning strategies (SRLSs), and AI literacy. The aim is to enhance human capital efficiency and prepare students to tackle future workplace challenges effectively. To examine these connections, a cross-sectional survey was administered to 1056 university students. The findings reveal that satisfying the three psychological needs—perceived autonomy, competence, and relatedness—plays a pivotal role in advancing AI literacy among university students. Additionally, four SRLSs—cognitive engagement, metacognitive knowledge, resource management, and motivational beliefs—acted as mediators between these psychological needs and AI literacy. Consequently, this study not only enhances our understanding of the psychological and behavioral development of university students during their engagement with AI education but also provides theoretical support and practical guidance for fostering their AI literacy.