In the next generation of Cloud computing systems, it is expected that multiple Cloud Service Providers (CSPs) will cooperate together to advertise their services and prices to their end users, which may choose the one that best meets their budgetary and technical needs. Despite this benefit of having multiple CSPs to select from, several issues may arise. For instance, how does an IT entrepreneur select a CSP to offload his/her service request? How does the underlying Inter-Cloud system handle this service request? To address these questions, this thesis proposes a novel Optimal Cloud Broker design for Inter-Cloud Systems in the form of a Semi-Markov Decision Process (SMDP) based model. Under the long-run expected average cost criterion, the optimal policy is derived, which aim at maximizing the overall virtual machine utilization while giving the end users the best possible prices. The effectiveness of the proposed Broker design is validated by numerical results.