We present a new method of accurately forecasting large geomagnetic storms (onset time, duration, and magnitude) exceeding a specified threshold in magnitude and the resulting global ionospheric dynamics in three dimensions (3D) as a function of time. The method uses solar wind (SW) data obtained at 1 AU (L1) as input and produces the spatial distribution and temporal evolution of predicted ionospheric quantities such as the total electron content (TEC) and polar cap potential (PCP) around the globe. The predicted warning time ranges from a few hours to more than 10 hours. The algorithm consists of three major components that are integrated together: (1) prediction of the interplanetary magnetic field (IMF) upstream of the 1 AU monitor, (2) simulation of the global magnetosphere in response to the predicted geoeffective SW structure, and (3) simulation of the ionospheric dynamics driven by the simulated magnetospheric dynamics. All three components are well established numerical codes. In particular, the method of predicting geoeffective SW structures (Step 1) has been field-tested at the Space Environment Center (SEC) and has been found to have a 70-80% accuracy rate. The SW-magnetosphere (LFM) model (Step 2) and the ionospheric (SAMI3) model (Step 3) are coupled, and a comparison of SAMI3 TEC results with data shows good agreement. The algorithm consists of an input matrix of SW parameters and an output matrix of the predicted spatial distribution and temporal evolution of ionospheric quantities corresponding to the input matrix elements. The output matrix is constructed using the coupled LFM-SAMI3 model. In the operational mode, the time required to make predictions using real-time SW data is minutes.