Although treatment for cholera is well-known and cheap, outbreaks in epidemic regions still exact high death tolls mostly due to the unpreparedness of health care infrastructures to face unforeseen emergencies. In this context, mathematical models for the prediction of the evolution of an ongoing outbreak are of paramount importance. Here, we test a real-time forecasting framework that readily integrates new information as soon as available and periodically issues an updated forecast. The spread of cholera is modeled by a spatially-explicit scheme that accounts for the dynamics of susceptible, infected and recovered individuals hosted in different local communities connected through hydrologic and human mobility networks. The framework presents two major innovations for cholera modeling: the use of a data assimilation technique, specifically an ensemble Kalman filter, to update both state variables and parameters based on the observations, and the use of rainfall forecasts to force the model. The exercise of simulating the state of the system and the predictive capabilities of the novel tools, set at the initial phase of the 2010 Haitian cholera outbreak using only information that was available at that time, serves as a benchmark. Our results suggest that the assimilation procedure with the sequential update of the parameters outperforms calibration schemes based on Markov chain Monte Carlo. Moreover, in a forecasting mode the model usefully predicts the spatial incidence of cholera at least for one month ahead. The performance decreases for longer time horizons yet allowing sufficient time to plan for deployment of medical supplies and staff, and to evaluate alternative strategies of emergency management.