Recent findings suggest that prism adaptation can extend its effects beyond spatial attention, modulating the performance of different cognitive tasks by acting on cerebellar, parietal and temporal-frontal networks. We tested groups of healthy subjects to investigate the effects of rightward vs. leftward prism adaptation vs. neutral lenses exposure in a series of memory tasks, probing either short-term (Digit span, Corsi span) or long-term memory (Supraspan verbal and spatial learning). In the short-term memory tasks, leftward prism adaptation selectively increased verbal span, while rightward prism adaptation increased spatial span. In the long-term memory tasks, leftward prism adaptation selectively increased verbal supraspan, i.e., increased the number of digits in the correct sequence reproduced and reduced the number of repetitions needed to learn the supraspan sequence. On the other hand, rightward prism adaptation selectively increased spatial supraspan, i.e. it increased the number of spatial positions in the correct sequence reproduced and reduced the number of repetitions needed to learn the supraspan sequence. Moreover, rightward, but not leftward, prism adaptation selectively increased supraspan recall after a delay interval, regardless of the stimulus material, i.e., it increased the number of digits or spatial positions recalled after a delay interval. Neutral lenses exposure did not influence any memory task. These findings suggest that prism adaptation can induce both modality/hemispheric-specific and process-specific effects on short-term and long-term explicit memory.