Cloud computing services (CCS) offer many benefits which have improved their acceptance in the educational sector, especially, tertiary education. While it is true that the benefits of CCS include less worries about data loss, ease of accessibility and the ability to interact with data in real-time, there is no known study on how awareness of cloud computing services, perceived ease of use, computer self-efficacy, and intention to use CCS influence its actual use among postgraduate students in Nigeria. This study provides answers to four research questions and tests two research hypotheses. It adopts a descriptive survey design using a multistage sampling technique for data collection. Convenience sampling technique was used to select a sample size of 360 postgraduate students from the University of Ibadan, Nigeria. Descriptive statistics, Friedman mean rank, Spearman rank correlation and Multiple linear regression were used for analyses. The findings revealed that awareness of cloud computing services, perceived ease of use, and computer self-efficacy had significant relationships with the intention to use cloud computing services, and the intention to use cloud computing services had a significant influence on the actual use of cloud computing services among postgraduate students. The study recommends that university authorities should encourage courses that train students on the use of CCS, as well as course curricula to improve students’ computer self-efficacy and their use of cloud computing services. Keywords: Awareness, Cloud Computing, Self-Efficacy, Intention to Use, Perceived Ease of Use, Postgraduate students, Cloud Computing Services, University of Ibadan, Nigeria