This research explores the quickly changing field of generative artificial intelligence (GAI) chatbots in higher education, an industry that is undergoing major technological changes. AI chatbots, such as ChatGPT, HuggingChat, and Google Bard, are becoming more and more common in a variety of sectors, including education. Their acceptance is still in its early phases, with a variety of prospects and obstacles. However, their potential in higher education is particularly noteworthy, providing lecturers and students with affordable, individualized support. Creating a comprehensive framework to aid the usage of generative AI chatbots in higher education institutions (HEIs) is the aim of this project. The Generative AI Chatbots Acceptance Model (GAICAM) is the result of this study's synthesis of elements from well-known frameworks, including the TAM, UTAUT2, TPB, and others along with variables like optimism, innovativeness, discomfort, insecurity, and others. Using a research method that encompasses a comprehensive analysis of extant literature from databases such as IEEE, ACM, ScienceDirect, and Google Scholar, the study aims to comprehend the implications of AI Chatbots on higher education and pinpoint critical elements for their efficacious implementation. Peer-reviewed English-language publications published between 2020 and 2023 with a focus on the use of AI chatbots in higher education were the main focus of the search criteria. The results demonstrate how much AI chatbots can do to improve student engagement, streamline the educational process, and support administrative and research duties. But there are also clear difficulties, such as unfavorable student sentiments, doubts about the veracity of material produced by AI, and unease and nervousness with new technologies.