ChatGPT, a widely used generative AI tool, has incessantly attracted significant attention from researchers seeking to understand the factors that influence its adoption in higher education. This study examined the determinants of ChatGPT adoption among university students in Yogyakarta, Indonesia, one of the largest educational centers with more than 100 higher education institutions. Drawing on the value-based adoption model (VAM), the study incorporated three AI-related factors, i.e., AI self-efficacy (ASE), perceived academic value (PAV), and privacy concerns (PC) to appropriately explain students’ behavior in AI adoption. A hybrid analytical approach combining partial least squares structural equation modeling (PLS-SEM) and machine learning (ML) techniques, including Random Forest (RF), eXtreme Gradient Boosting (XGBoost), and Artificial Neural Networks (ANN) with SHapley Additive exPlanations (SHAP)-based interpretation, was employed to test ten hypotheses with survey data collected from 484 students across five selected universities in Yogyakarta. The results indicated that perceived value (PV) (β = 0.453) and adoption intention (β = 0.521) were the strongest predictors of actual ChatGPT usage. Among the benefit-related factors, perceived usefulness (PU), perceived enjoyment (PE), and ASE significantly enhanced PV, whereas PC (β = −0.213) represented the most influential barrier to adoption. The ML models produced consistent findings, with XGBoost achieving the highest predictive performance (AUC = 0.912). SHAP analysis further highlighted PV and PC as the most significant variables. By extending VAM with AI-specific constructs and integrating SEM with ML techniques, this study contributes to an enhanced understanding of generative AI adoption in higher education and offers actionable insights for policymakers and university administrators in support of responsible AI integration in Indonesian universities.