Over the years, there has been a significant evolution in telecommunication technology, in particular the Third Generation Partnership Project (3GPP) family of telecommunication systems. The demand for broadband wireless Internet has been the main catalyst, hence we now have the fourth generation (4G). Similarly, there has been a paradigm shift in the computing world towards cloud computing, both by individual users as well as private and public institutions. The purpose of this thesis therefore, was to explore the 4G Long Term Evolution (4G LTE) as well as the cloud computing technology and highlight the convergence of these techonologies and their applications in various fields. Courtesy of the 3GPP, the technical specifications for Long Term Evolution (LTE) and LTE-Advanced (LTE-Advanced) were outlined. In this thesis therefore, these specifications along with other related publications, and in addition, publications about the cloud computing technology were explored for insight. The convergence of 4G and cloud computing, some (4G and cloud computing) solutions for telecommunication operators and a few applications of 4G LTE and cloud computing were brought to the fore. This thesis as a result, presented the case for the adoption of 4G LTE and cloud computing to complement each other. It has also highlighted available technological solutions for telecommunication operators for cloud computing and also outlined some examples where the technologies can be applied in tandem. In future, experiments can be carried out to test the various applications of these technologies.