The introduction of cloud computing techniques revolutionized the current of information processing and storing. Cloud computing as a competitive edge provides easy and automated access to the vast ocean of resources through standard network mechanisms to businesses and organizations. Due to the vast diversity of service providers and their respective variety of available services with different qualities, top managements often face difficulty for choosing the best available option. So, considering the growing significance of the mentioned issue, this study aims to identify and rank contributing factors in selection of cloud service providers. In that attempt, this research approaches its goal by going through three major phases. Firstly, in phase one, prior studies are reviewed for extracting related elements of selection. Secondly, by employing Fuzzy Delphi method and obtaining results by interviewing experts in this field such as IT managers and technicians, this study tries to finalize the list of contributing factors. Lastly, by utilizing Fuzzy best-worst multi-criteria decision-making method, which is one of the most recent techniques employed to statistically rank variables, this research introduces a list of vital factors for cloud service selection. Based on the findings of this study, there are five major categories involved in the selection process which are: performance, security, data management, personal data protection and environmental-organizational. The finalized result of ranking shows that, performance related factors such as accessibility, response time and capacity are the first priority. The runner-up is security with reliability and governance. Environmental-organizational variables lands in the third place by considering rental and network costs.