The future of healthcare systems is being shaped by incorporating emerged technological innovations to drive new models for patient care. By acquiring, integrating, analyzing, and exchanging medical data at different system levels, new practices can be introduced, offering a radical improvement to healthcare services. This paper presents a novel smart and secure Healthcare system (ssHealth), which, leveraging advances in edge computing and blockchain technologies, permits epidemics discovering, remote monitoring, and fast emergency response. The proposed system also allows for secure medical data exchange among local healthcare entities, thus realizing the integration of multiple national and international entities and enabling the correlation of critical medical events for, e.g., emerging epidemics management and control. In particular, we develop a blockchain-based architecture and enable a flexible configuration thereof, which optimize medical data sharing between different health entities and fulfil the diverse levels of Quality of Service (QoS) that ssHealth may require. Finally, we highlight the benefits of the proposed ssHealth system and possible directions for future research.