Crop management has a significant impact on crop yield, economic profit, and the environment. Although management guidelines exist, finding the optimal management practices is challenging. Previous work used reinforcement learning (RL) and crop simulators to solve the problem, but the trained policies either have limited performance or are not deployable in the real world. In this paper, we present an intelligent crop management system that optimizes nitrogen fertilization and irrigation simultaneously via RL, imitation learning (IL), and crop simulations using the Decision Support System for Agrotechnology Transfer (DSSAT). We first use deep RL, in particular, deep Q-network, to train management policies that require a large number of state variables from the simulator as observations (denoted as full observation). We then invoke IL to train management policies that only need a few state variables that can be easily obtained or measured in the real world (denoted as partial observation) by mimicking the actions of the RL policies trained under full observation. Simulation experiments using the maize crop in Florida (US) and Zaragoza (Spain) demonstrate that the trained policies from both RL and IL techniques achieved more than 45\% improvement in economic profit while causing less environmental impact compared with a baseline method. Most importantly, the IL-trained management policies are directly deployable in the real world as they use readily available information.