The digital transformation of electric power systems requires forecasts and planning for optimal management, as well as real-time data streaming for the ongoing optimization of the system during operation. Recent research efforts have developed models for power system capacity planning, real-time monitoring and control, fault analysis, and energy efficiency assessment. However, those models are usually not integrated and do not combine operational data with management information and real-time decision-making. This paper conceives a data-driven model that integrates optimization and machine learning techniques for optimal operation and management of prosumer markets in electric smart grids. While classical optimization is used during day-ahead mode for operation planning, Gaussian Processes are used to predict demand forecasts for day-ahead and pre-dispatch modes while assimilating real-time measurements. The proposed approach is applied in a case study comprising a community manager coordinating a smart grid with prosumers operating thermal and renewable generators. Results highlight that the data-driven model helps achieve near-optimal operation of the smart grid in normal conditions while guaranteeing its reliability under disruptive events.