Crop yield information at field scale is important for farmers, crop insurance companies and agricultural communities in general. In this study, a wide range of ground-collected yield data was used to develop crop yield forecast models for the two internationally important crops: wheat and soybeans. A deep neural network (NN), a long short-term memory (LSTM), was trained for both crops individually. For each crop, the LSTM model was trained for two different scenarios including using Synthetic Aperture Radar (SAR)-only data as first scenario and using integration of SAR and optical satellite data as a second scenario. The root mean square error (RMSE) and coefficient of determination $(R^{2})$ were estimated for each scenario. The results demonstrated that the accuracies improved from RMSE of 516.7 kg/ha and $R^{2}$ of 0.79 (scenario 1) to RMSE of 433.77 kg/ha and $R^{2}$ of 0.87 (scenario 2) for soybeans. For wheat, the accuracies improved from RMSE of 617.14 kg/ha and $R^{2}$ of 0.83 (scenario 1) to RMSE of 423.04 kg/ha and $R^{2}$ of 0.87 (scenario 2). These results show that using SAR data and their integration with optical satellite data is a promising approach for crop yield forecast at field scale.