In the ever-evolving AI-driven education, integrating AI technologies into teaching practices has become increasingly imperative for aspiring STEM educators. Yet, there remains a dearth of studies exploring pre-service STEM teachers' readiness to incorporate AI into their teaching practices. This study examined the factors influencing teachers' willingness to integrate AI (WIAI), especially from the perspective of pre-service STEM teachers' attitudes towards the application of AI in teaching. In the study, a comprehensive survey was conducted among 239 pre-service STEM teachers, examining the influences and interconnectedness of Technological Pedagogical Content Knowledge (TPACK), Perceived Usefulness (PU), Perceived Ease of Use (PE), and Self-Efficacy (SE) on WIAI. Structural Equation Modeling (SEM) was employed for data analysis. The findings illuminated direct influences of TPACK, PU, PE, and SE on WIAI. TPACK was found to directly affect PE, PU, and SE, while PE and PU also directly influenced SE. Further analysis revealed significant mediating roles of PE, PU, and SE in the relationship between TPACK and WIAI, highlighting the presence of a chain mediation effect. In light of these insights, the study offers several recommendations on promoting pre-service STEM teachers' willingness to integrate AI into their teaching practices.