As artificial intelligence (AI) technologies become increasingly embedded in higher education, concerns have emerged regarding their psychological impact on university faculty. While existing research has largely focused on technological readiness and digital competencies, the social–psychological foundations of faculty well-being in AI-integrated teaching environments remain insufficiently explored. Drawing on social support theory and self-determination theory, this study proposes and tests a structural model of AI-related well-being among university faculty. A total of 523 faculty members in China participated in a cross-sectional survey measuring perceived social support, organizational support, AI literacy, technological self-efficacy, and AI well-being. Structural equation modeling (SEM) was used to examine the hypothesized pathways and mediating mechanisms. The results indicate that both social support and organizational support significantly and positively influence AI literacy and technological self-efficacy. In turn, AI literacy and technological self-efficacy significantly predict AI well-being and serve as key mediators. Among all factors, AI literacy exhibits the strongest total effect on AI well-being, followed by social support, organizational support, and technological self-efficacy. This study contributes to the theoretical understanding of faculty psychological adjustment during technological transitions and offers practical recommendations for institutions seeking to cultivate AI-ready and psychologically supportive academic environments.