The examination of the impact of Generative AI (GenAI) on higher education, especially from the viewpoint of students, is gaining significance. Although prior research has underscored GenAI's potential advantages in higher education, there exists a discernible research gap concerning the determinants that affect its adoption. In the present study, we aim to enhance our comprehension of the factors influencing the willingness of higher education students to adopt GenAI tools. To achieve this, we have developed an extended Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) model incorporating specific GenAI constructs. Our research methodology entailed the selection of a diverse sample of 374 students through random sampling. We then analyzed their data using Structural Equation Modeling (SEM) to gain insights into the complex relationships between various variables. The study found that students are more likely to use GenAI tools when they view them as supplemental resource and effort expectancy. It also revealed that perceived costs negatively impact adoption intentions, highlighting that financial factors are a significant barrier. Interestingly, Factors like information accuracy and hedonic motivation did not significantly affect students' adoption intentions. This study offers key insights for eLearning practitioners on integrating Generative AI (GenAI) tools into educational settings. It emphasizes the significance of resource perception and effort expectancy, demonstrating GenAI's potential to personalize learning experiences. eLearning platforms can utilize GenAI to enhance active learning through engaging methods and streamline course development. Addressing cost barriers is crucial for equitable access and inclusivity. A gradual approach to integration aligned with learning objectives is recommended, along with fostering critical engagement with GenAI tools to enhance digital literacy. Lastly, the study is constrained by its specific context, potential biases in self-reported data, a narrow focus on factors influencing students' intent to use GenAI tools and a cross-sectional design. Future research should encompass a broader range of factors, employ objective measures, and integrate observational data. Longitudinal studies or experimental designs could offer more comprehensive insights into how students' perceptions and intentions develop, thus promoting a more inclusive educational environment for all students.