Epidural electrical stimulation (EES) of lumbosacral segments can restore a range of movements after spinal cord injury. However, the mechanisms and neural structures through which EES facilitates movement execution remain unclear. Here, we designed a computational model and performed in vivo experiments to investigate the type of fibers, neurons, and circuits recruited in response to EES. We first developed a realistic finite element computer model of rat lumbosacral segments to identify the currents generated by EES. To evaluate the impact of these currents on sensorimotor circuits, we coupled this model with an anatomically realistic axon-cable model of motoneurons, interneurons, and myelinated afferent fibers for antagonistic ankle muscles. Comparisons between computer simulations and experiments revealed the ability of the model to predict EES-evoked motor responses over multiple intensities and locations. Analysis of the recruited neural structures revealed the lack of direct influence of EES on motoneurons and interneurons. Simulations and pharmacological experiments demonstrated that EES engages spinal circuits trans-synaptically through the recruitment of myelinated afferent fibers. The model also predicted the capacity of spatially distinct EES to modulate side-specific limb movements and, to a lesser extent, extension versus flexion. These predictions were confirmed during standing and walking enabled by EES in spinal rats. These combined results provide a mechanistic framework for the design of spinal neuroprosthetic systems to improve standing and walking after neurological disorders.