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Due to limited resolution and inaccurate physical parameterizations, weather and climate models consistently develop biases compared to the observed atmosphere. Using the FV3GFS model at coarse resolution, we propose a method of machine learning corrective tendencies from a hindcast simulation nudged toward observational analysis. We show that a random forest can predict the nudging tendencies from this hindcast simulation with moderate skill using only the model state as input. This random forest is then coupled to FV3GFS, adding corrective tendencies of temperature, specific humidity and horizontal winds at each timestep. The coupled model shows no signs of instability in year‐long simulations and has significant reductions in short‐term forecast error for 500 hPa height, surface pressure and near‐surface temperature. Furthermore, the root mean square error of the annual‐mean precipitation is reduced by about 20%. Biases of other variables remain similar or in some cases, like upper‐atmospheric temperature, increase in the year‐long simulations. After initialization from a realistic snapshot of the atmosphere, weather and climate models inevitably develop prediction errors compared to the real world. This decreases the usefulness of forecasts. These errors arise from the coarse resolution of the numerical models and from the uncertain treatment of small‐scale processes. We propose a method to reduce these errors by training a machine learning model to correct for them as the atmospheric model proceeds. We show that a random forest can make reasonably skillful predictions of the required correction using a snapshot of the model state as input. When we make a forecast with the machine‐learning corrected model, equally skillful predictions of important midtropospheric and surface variables are possible half‐a‐day to a day further into the future. The pattern of precipitation predicted by the machine learning corrected model is also more realistic, with a decrease in excessive rainfall over high mountains. On the other hand, the corrected model develops larger errors in temperature in the high latitudes, particularly in the lower stratosphere. Nudging an atmospheric model toward observations is a good way to estimate state‐dependent biasesMachine learning of state‐dependent biases improves hindcast skill of a coarse‐resolution general circulation model (GCM)Bias‐corrected year‐long simulations are stable and reduce time‐mean precipitation pattern errors Nudging an atmospheric model toward observations is a good way to estimate state‐dependent biases Machine learning of state‐dependent biases improves hindcast skill of a coarse‐resolution general circulation model (GCM) Bias‐corrected year‐long simulations are stable and reduce time‐mean precipitation pattern errors