Regaining arm control is a top priority for people with paralysis. Unfortunately, the complexity of the neural mechanisms underlying arm control has limited the effectiveness of neurotechnology approaches. Here, we exploited the neural function of surviving spinal circuits to restore voluntary arm and hand control in three monkeys with spinal cord injury, using spinal cord stimulation. Our neural interface leverages the functional organization of the dorsal roots to convey artificial excitation via electrical stimulation to relevant spinal segments at appropriate movement phases. Stimulation bursts targeting specific spinal segments produced sustained arm movements, enabling monkeys with arm paralysis to perform an unconstrained reach-and-grasp task. Stimulation specifically improved strength, task performances and movement quality. Electrophysiology suggested that residual descending inputs were necessary to produce coordinated movements. The efficacy and reliability of our approach hold realistic promises of clinical translation.