The complex mechanics of the arm make the neural control of reaching inherently posture dependent. Because previous reaching studies confound reach direction with final posture, it remains unknown how neural population dynamics in the motor cortex account for arm posture. Here we address this gap with high-density neural recordings and a reaching task in which the same targets serve as start points on some trials and end points on others. We show that neural population dynamics in monkey primary motor cortex and dorsal premotor cortex exhibit a compositional structure with three components that enable posture-dependent control: first, a posture subspace containing fixed points visited whenever the arm is in a specific posture; second, rotational dynamics that transition between these fixed points, systematically organized so that similar rotations produce similar movements while continuously updating the posture representation; third, a condition-independent shift dimension that tracks trial progression across all movements. This compositional structure advances the population-level account of how motor cortical dynamics support skilled reaching.