EUropean Heliospheric FORecasting Information Asset (EUHFORIA) is a physics‐based data‐driven solar wind and coronal mass ejections (CMEs) propagation model designed for space weather forecasting and event analysis investigations. Although EUHFORIA can predict the solar wind plasma and magnetic field properties at Earth, it is not equipped to quantify the geo‐effectiveness of the solar transients in terms of geomagnetic indices like the disturbance storm time (Dst) index and the auroral indices, that quantify the impact of the magnetized plasma encounters on Earth's magnetosphere. Therefore, we couple EUHFORIA with the Open Geospace General Circulation Model (OpenGGCM), a magnetohydrodynamic model of the response of Earth's magnetosphere, ionosphere, and thermosphere to transient solar wind characteristics. In this coupling, OpenGGCM is driven by the solar wind and interplanetary magnetic field obtained from EUHFORIA simulations to produce the magnetospheric and ionospheric response to the CMEs. This coupling is validated with two observed geo‐effective CME events driven with the spheromak flux‐rope CME model. We compare these simulation results with the indices obtained from OpenGGCM simulations driven by the measured solar wind data from spacecraft. We further employ the dynamic time warping (DTW) technique to assess the model performance in predicting Dst. The main highlight of this study is to use EUHFORIA simulated time series to predict the Dst and auroral indices 1–2 days in advance, as compared to using the observed solar wind data at L1, which only provides predictions 1–2 hr before the actual impact.