The integration of artificial intelligence (AI) has become widespread, particularly with the popularisation of generative AI (genAI) technologies across various sectors. In higher education, the adoption and integration of genAI has given rise to debates concerning its potential impact on future teaching and learning experiences, which has motivated several empirical studies. However, these studies have adopted only partial explanatory models. Considering this, the present study aims to explore the factors that influence higher education students’ acceptance and adoption of genAI, using the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) framework. A cross-sectional design was employed, involving a sample of 339 higher education students. PLS-SEM analysis showed a positive relationship between performance expectancy, social influence, facilitating conditions, hedonic motivation, and habit, and students’ intention to use genAI, and in addition behavioural intention is a key determinant of actual use. Notably, effort expectancy and price value were not found to be significant predictors. These results provide a comprehensive framework for understanding student behaviour, offering a foundation for strategies for universities and educators seeking to integrate these technologies ethically and effectively. The study underscores the importance of focusing on the users’ perspective to ensure successful technological integration in academic settings.