Domestic hot water (DHW) heating accounts for up to 30% of average household energy use. Compared to gas fired water heaters, electric water heaters (EWH) can be powered by renewable generation resources, thus making it a potential renewable heating option. Furthermore, with the growing need for energy storage, incorporation of renewable resources, and initiatives worldwide, the electrification of DHW heating is expected to continue the rapid growth. However, many commercial EWH products with monitoring and alerting functionalities lack the intelligence to optimize and perform predictive control with data; on the other hand, research studies with refined models and simulations come short in incorporating real-time data and providing robust optimal controls under uncertainties in real-world settings. This paper presents a EWH Smart Scheduling and Control System using data-driven disturbance forecasts in a robust Model Predictive Control (MPC) to accomplish various demand side management objectives. Testing with a real-world EWH dataset and a two-state EWH model, robust MPC simulations are conducted on a central EWH supplying DHW for a multi-unit apartment building with quantified prediction uncertainty. Results show that the proposed system is capable of anticipating DHW demand with an uncertainty interval covering up to 97% of the actual demand during the test days and reducing electricity cost up to 33.2% as well as maintaining a desired DHW temperature without affecting user comfort. Further, the flexibility of the system to alter load profiles under different Demand Response (DR) programs is demonstrated. Reductions in both power and water consumption can be accomplished. The proposed system can create an implementable solution of forecasting DHW usage and optimizing controls as a part of a robust and reliable building energy management and control system in real-world settings.