Migrating organisational services, data and application on the Cloud is an important strategic decision for organisations due to the large number of benefits introduced by the usage of cloud computing, such as cost reduction and on demand resources. Despite, however, of the many benefits, there are challenges and risks for cloud adaption related to (amongst others) data leakage, insecure APIs, and shared technology vulnerabilities. These challenges need to be understood and analysed in the context of an organisation relevant cloud computing deployment models. Although, the literature provides a large number of references to works that consider cloud computing security issues, no work has been provided, to our knowledge, which supports the elicitation of security and privacy requirements and the selection of an appropriate cloud deployment model based on such requirements. This work contributes towards this gap. In particular, we propose a requirements engineering framework to support the elicitation of security and privacy requirements and the selection of an appropriate deployment model based on the elicited requirements. Our framework provides a modelling language that builds on concepts from requirements, security, privacy and cloud engineering and a systematic process. We use a real case study, based on the Greek National Gazette, to demonstrate the applicability of our work.