To navigate in the world, an animal’s brain must produce commands to move, change direction, and negotiate obstacles. In the insect brain, the central complex integrates multiple forms of sensory information and guides locomotion during behaviors such as foraging, climbing over barriers, and navigating to memorized locations. These roles suggest that the central complex influences motor commands, directing the appropriate movement within the current context. Such commands are ultimately carried out by the limbs and must therefore interact with pattern generators and reflex circuits that coordinate them. Recent studies have described how neurons of the central complex encode sensory information: neurons subdivide the space around the animal, encoding the direction or orientation of stimuli used in navigation. Does a similar central-complex code directing movement exist, and if so, how does it effect changes in the control of limbs? Recording from central-complex neurons in freely walking cockroaches (Blaberus discoidalis), we identified classes of movement-predictive cells selective for slow or fast forward walking, left or right turns, or combinations of forward and turning speeds. Stimulation through recording wires produced consistent trajectories of forward walking or turning in these animals, and those that elicited turns also altered an inter-joint reflex to a pattern resembling spontaneous turning. When an animal transitioned to climbing over an obstacle, the encoding of movement in this new context changed for a subset of cells. These results indicate that encoding of movement in the central complex participates in motor control by a distributed, flexible code targeting limb reflex circuits.