When the brain initiates a saccade, it uses a copy of the oculomotor commands to predict the visual consequences: for example, if one fixates a reach target, a peripheral saccade will produce an internal estimate of the new retinal location of the target, a process called remapping. In natural settings, the target likely remains visible after the saccade. So why should the brain predict the sensory consequence of the saccade when after its completion, the image of the target remains visible? We hypothesized that in the post-saccadic period, the brain integrates target position information from two sources: one based on remapping and another based on the peripheral view of the target. The integration of information from these two sources could produce a less variable target estimate than is possible from either source alone. Here, we show that reaching toward targets that were initially foveated and remapped had significantly less variance than reaches relying on peripheral target information. Furthermore, in a more natural setting where both sources of information were available simultaneously, variance of the reaches was further reduced as predicted by integration. This integration occurred in a statistically optimal manner, as demonstrated by the change in integration weights when we manipulated the uncertainty of the post-saccadic target estimate by varying exposure time. Therefore, the brain predicts the sensory consequences of motor commands because it integrates its prediction with the actual sensory information to produce an estimate of sensory space that is better than possible from either source alone.