Owning and managing a cloud-computing infrastructure, i.e. private data centers (DC), is a feasible way forward for an organization to ensure security of data when opting for cloud computing services. However, the cost associated with operating and managing a DC is a challenge because of the huge amount of power consumed and the carbon dioxide added to the environment. In particular, Higher Learning Institutions in Tanzania (HLIT) are among the institutions which need efficient computing infrastructure. This paper proposes eco-efficient cloud computing building blocks that ensure environment protection and optimal operational costs of a cloud computing framework that suffices HLIT computing needs. The proposed building blocks are in a form of power usage (renewable and nonrenewable); cloud deployment model and data center location; ambient climatic conditions and data center cooling; network coverage; quality of service and HLIT cloud software. The blocks are identified by considering HLIT computing requirements and challenges that exist in managing and operating cloud data centers. Moreover, this work identifies the challenges associated with optimization of resource usage in the proposed approach; and suggests related solutions as future work.