How does the motor cortex (MC) produce purposeful and generalizable movements from the complex musculoskeletal system in a dynamic environment? To elucidate the underlying neural dynamics, we use a goal-driven approach to model MC by considering its goal as a controller driving the musculoskeletal system through desired states to achieve movement. Specifically, we formulate the MC as a recurrent neural network (RNN) controller producing muscle commands while receiving sensory feedback from biologically accurate musculoskeletal models. Given this real-time simulated feedback implemented in advanced physics simulation engines, we use deep reinforcement learning to train the RNN to achieve desired movements under specified neural and musculoskeletal constraints. Activity of the trained model can accurately decode experimentally recorded neural population dynamics and single-unit MC activity, while generalizing well to testing conditions significantly different from training. Simultaneous goal- and data- driven modeling in which we use the recorded neural activity as observed states of the MC further enhances direct and generalizable single-unit decoding. Finally, we show that this framework elucidates computational principles of how neural dynamics enable flexible control of movement and make this framework easy-to-use for future experiments.