Many cells in retinotopic brain areas increase their activity when saccades (rapid eye movements) are about to bring stimuli into their receptive fields. Although previous work has attempted to look at the functional correlates of such predictive remapping, no study has explicitly tested for better attentional performance at the future retinal locations of attended targets. We found that, briefly before the eyes start moving, attention drawn to the targets of upcoming saccades also shifted to those retinal locations that the targets would cover once the eyes had moved, facilitating future movements. This suggests that presaccadic visual attention shifts serve to both improve presaccadic perceptual processing at the target locations and speed subsequent eye movements to their new postsaccadic locations. Predictive remapping of attention provides a sparse, efficient mechanism for keeping track of relevant parts of the scene when frequent rapid eye movements provoke retinal smear and temporal masking.