Cloud computing has developed in popularity as a large-scale computing paradigm that offers a range of computing resources as a service through the internet on a pay-as-you-go basis. The expansion in demand and commercial availability of cloud services brings new challenges to cloud services selection. Several research studies have been conducted to develop enhanced methodologies to assist service consumers in selecting appropriate services. In this paper, 105 primary studies published during January, 2011 to May, 2022 has been selected using a multi-stage scrutinizing approach. The selected preliminary studies were further classified based on various variables to answer the research questions stated for this work. A systematic review of existing cloud service selection approaches is performed, which are analyzed along eight dimensions: decision-making methods, context, purposes, cloud service performance parameters, simulation/language tools, domain, datasets, and experiment/validation methods. After a thorough review and comparison of these approaches across the above-mentioned dimensions, several open research issues in the current literature have been identified. The contribution of this research is fourfold: focusing on state-of-the-art cloud services selection approaches, highlighting the benefits and drawbacks of various cloud services selection methodologies and their future directions, offering a taxonomy based on a thorough literature study, and identifying nine critical challenges in cloud services selection that require further investigation. This systematic review study is anticipated to benefit both academics and business experts.