Crop yield prediction is extremely challenging due to its dependence on multiple factors such as crop genotype, environmental factors, management practices, and their interactions. This paper presents a deep learning framework using convolutional neural networks (CNNs) and recurrent neural networks (RNNs) for crop yield prediction based on environmental data and management practices. The proposed CNN-RNN model, along with other popular methods such as random forest (RF), deep fully connected neural networks (DFNN), and LASSO, was used to forecast corn and soybean yield across the entire Corn Belt (including 13 states) in the United States for years 2016, 2017, and 2018 using historical data. The new model achieved a root-mean-square-error (RMSE) 9% and 8% of their respective average yields, substantially outperforming all other methods that were tested. The CNN-RNN has three salient features that make it a potentially useful method for other crop yield prediction studies. (1) The CNN-RNN model was designed to capture the time dependencies of environmental factors and the genetic improvement of seeds over time without having their genotype information. (2) The model demonstrated the capability to generalize the yield prediction to untested environments without significant drop in the prediction accuracy. (3) Coupled with the backpropagation method, the model could reveal the extent to which weather conditions, accuracy of weather predictions, soil conditions, and management practices were able to explain the variation in the crop yields.