When we are able to prepare in advance of a movement, the subsequent movements generally get better. Motor cortical activity during preparation has been studied extensively, showing clear relationships between the neural population state achieved during preparation and the parameters of the subsequent self-initiated movement. However, movements are often triggered or corrected based on disturbances to the body or environment. Since such disturbances can often be predicted based on experience or other streams of sensory input, we reasoned that sensory expectations should also shape preparatory activity in motor cortical areas. Here we show that when humans and monkeys are visually cued about the probability of the direction of future mechanical perturbations, they readily incorporate sensory expectations into their movement preparation, improving perturbation responses by better tuning transcortical feedback responses. Using high-density neural recordings in monkeys, we establish that information about sensory expectations is widespread across many brain areas. The geometry of these probability signals is simple, scaling directly with the probability of each perturbation direction. On the other hand, when sensory expectations are acquired through experience as opposed to being visually cued, only some areas (PMd, M1, SMA) show the same neural geometry. Based on neural networks coupled to a biomechanical model of the arm, we show that this simple neural geometry emerges through training and is beneficial for countering disturbances. Crucially, sensory expectations can only be used to improve perturbation responses when the timing of incoming sensory information indicating the direction of a perturbation coincides closely with condition-independent signals indicating that a perturbation has been detected. These results broaden our understanding of motor control by demonstrating that expectations about future sensory input are a fundamental component of neural dynamics during reaching.