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Cloud computing has been regarded as one of the significant Information Technology (IT) tools. Many sectors are adopting cloud computing services for its business support. It has also become a new IT paradigm that has transformed the E-Learning system to become more user-friendly. As a result, the E-Learning usage is growing rapidly and being preferred over the conventional teaching-learning process in a big way. This revolutionary change is attributed to the advancement in digital technology. The transformation in digital technology has made the teaching-learning process flexible, easy and convenient for effective knowledge transfer. The cloud-based E-Learning process depends upon many factors of different dimensions that are of significant importance for cloud-based-E-Learning success. Hence they must be studied to successfully analyze their level of importance and fulfill Cloud-based E-Learning positive effectiveness. The current research provides a detailed literature review for cloud-based E-Learning Critical Success Factors (CSFs) of teaching-learning process. Further, the research employs the combinatorial approach to evaluate the diversified dimensions and CSFs of cloud-based E-Learning that helps in quantifying and comparing the influence of various dimensions and CSFs of cloud-based-E-Learning. Four dimensions and fourteen factors have been identified through in-depth literature review and later on evaluated for the prioritization using a combinatorial approach. The influence of such dimensions and factors will help various stakeholders to plan their strategy and resources for the betterment of knowledge transfer through cloud-based-E-Learning.