Drawing on the Theory of Planned Behaviour (TPB), this study investigates the relationship between the perceived benefits, strengths, weaknesses, and risks of generative AI (GenAI) tools and the fundamental factors of the TPB model (i.e., attitude, subjective norms, and perceived behavioural control). The study also investigates the structural association between the TPB variables and intention to use GenAI tools, and how the latter might affect the actual usage of GenAI tools in higher education. The paper adopts a quantitative approach, relying on an anonymous self-administered online questionnaire to gather primary data from 130 lecturers and 168 students in higher education institutions (HEIs) in several countries, and PLS-SEM for data analysis. The results indicate that although lecturers' and students' perceptions of the risks and weaknesses of GenAI tools differ, the perceived strengths and advantages of GenAI technologies have a significant and positive impact on their attitudes, subjective norms, and perceived behavioural control. The TPB core variables positively and significantly impact lecturers' and students’ intentions to use GenAI tools, which in turn significantly and positively impact their adoption of such tools. This paper advances theory by outlining the factors shaping the adoption of GenAI technologies in HEIs. It provides stakeholders with a variety of managerial and policy implications for how to formulate suitable rules and regulations to utilise the advantages of these tools while mitigating the impacts of their disadvantages. Limitations and future research opportunities are also outlined.