Harnessing the network slicing feature of the 5G architecture and the mobile cloud computing capabilities offered by Mobile Edge Computing (MEC), mobile edge communication systems are emerging that contribute to the convergence of telecom and cloud services. In this scenario, mobile edge slices can be created and deployed by leveraging multi-cloud infrastructure. However, it becomes difficult for potential users, such as mobile edge slice tenants, to evaluate and select the Cloud Infrastructure Provider (CIP) which best meets their heterogeneous requirements. Therefore, mobile edge systems require slice brokering to mediate with resource and infrastructure providers, so that mobile edge slice tenants can specify a single set of network and cloud service Key Performance Indicator (KPI) requirements. In this paper we present a new type of broker, the Mobile Edge Slice Broker, that allows designing, provisioning, and orchestrating the deployment and operation of end-to-end mobile edge slices over edge and multi-cloud environments, while maintaining dynamic monitoring, reconfiguration and optimization capabilities.