Cloud Computing is one of the latest revolutions in information technology that influences many sectors in many governments. Cloud computing is a model for providing resources for storage and communication based on the service as quickly as possible, that is virtually applied through internet access. Despite the concern shown by many countries in adopting cloud computing, not many researchers have shown what the most desirable factors are that influence key players in public sector to allow them to decide on cloud computing adoption. The existing researches indicated other areas such as accepting the cloud computing service in government organizations, establishing the architecture of cloud computing, and integrating the cloud computing services. Thus, the study has examined to prioritize adoption factors that have been considered the most desirable ones in effecting public sector adoption cloud computing by conducting a web- based survey in the Ministry of Higher Education in Iraq. From the results, the top management support, cloud strategy, IT infrastructure, compatibility, external expertise, and internal experts, are the most important factors for Iraqi government organizations to adopt cloud computing while complexity, trailability, competitive and cost factors are specified as the minor factors.