The frequent occurrence of saccadic eye movements raises the question of how information is combined across separate glances into a stable, continuous percept. Here I show that visual form processing is altered at both the current fixation position and the location of the saccadic target before the saccade. When human observers prepared to follow a displacement of the stimulus with the eyes, visual form adaptation was transferred from current fixation to the future gaze position. This transfer of adaptation also influenced the perception of test stimuli shown at an intermediate position between fixation and saccadic target. Additionally, I found a presaccadic transfer of adaptation when observers prepared to move their eyes toward a stationary adapting stimulus in peripheral vision. The remapping of visual processing, demonstrated here with form adaptation, may help to explain our impression of a smooth transition, with no temporal delay, of visual perception across glances.