Electronic Health (e-Health) technology has brought the world with significant transformation from traditional paper-based medical practice to Information and Communication Technologies (ICT)-based systems for automatic management (storage, processing, and archiving) of information. Traditionally e-Health systems have been designed to operate within stovepipes on dedicated networks, physical computers, and locally managed software platforms that make it susceptible to many serious limitations including: 1) lack of on-demand scalability during critical situations; 2) high administrative overheads and costs; and 3) in-efficient resource utilization and energy consumption due to lack of automation. In this paper, we present an approach to migrate the ICT systems in the e-Health sector from traditional in-house Client/Server (C/S) architecture to the virtualised cloud computing environment. To this end, we developed two cloud-based e-Health applications (Medical Practice Management System and Telemedicine Practice System) for demonstrating how cloud services can be leveraged for developing and deploying such applications. The Windows Azure cloud computing platform is selected as an example public cloud platform for our study. We conducted several performance evaluation experiments to understand the Quality Service (QoS) tradeoffs of our applications under variable workload on Azure.