Regaining arm motor control is critical for people with paralysis. Despite promising results on grasping, no technology could restore effective arm control. Here, we show that electrical stimulation of the cervical spinal cord enabled three monkeys with cervical spinal injury to execute functional arm movements. We designed an epidural interface that engaged surviving spinal circuits via the recruitment of large sensory afferents to produce movement. Simple stimulation bursts produced sustained joint movements which, triggered by movement-related intracortical signals, enabled monkeys with arm paralysis to perform an unconstrained, three-dimensional reach and grasp task. This restoration of voluntary motor control was enabled by the synergistic integration of spared descending commands and electrical stimulation within the spinal cord. The simplicity of this technology promises realistic clinical translation.