The widespread adoption of generative Artificial Intelligence (GenAI) tools in higher education has necessitated the development of appropriate and ethical usage guidelines. This study aims to explore and assess publicly available guidelines covering the use of GenAI tools in universities, following a predefined checklist. We searched and downloaded publicly accessible guidelines on the use of GenAI tools from the websites of the top 50 universities globally, according to the 2025 QS university rankings. From the literature on GenAI use guidelines, we created a 24-item checklist, which was then reviewed by a panel of experts. This checklist was used to assess the characteristics of the retrieved university guidelines. Out of the 50 university websites explored, guidelines were publicly accessible on the sites of 41 institutions. All these guidelines allowed for the use of GenAI tools in academic settings provided that specific instructions detailed in the guidelines were followed. These instructions encompassed securing instructor consent before utilization, identifying appropriate and inappropriate instances for deployment, employing suitable strategies in classroom settings and assessment, appropriately integrating results, acknowledging and crediting GenAI tools, and adhering to data privacy and security measures. However, our study found that only a small number of the retrieved guidelines offered instructions on the AI algorithm (understanding how it works), the documentation of prompts and outputs, AI detection tools, and mechanisms for reporting misconduct. Higher education institutions should develop comprehensive guidelines and policies for the responsible use of GenAI tools. These guidelines must be frequently updated to stay in line with the fast-paced evolution of AI technologies and their applications within the academic sphere.