Variability of above-ground net primary production (ANPP) of arid to sub-humid ecosystems displays a closer association with precipitation when considered across space (based on multiyear averages for different locations) than through time (based on year-to-year change at single locations). Here, we propose a theory of controls of ANPP based on four hypotheses about legacies of wet and dry years that explains space versus time differences in ANPP–precipitation relationships. We tested the hypotheses using 16 long-term series of ANPP. We found that legacies revealed by the association of current- versus previous-year conditions through the temporal series occur across all ecosystem types from deserts to mesic grasslands. Therefore, previous-year precipitation and ANPP control a significant fraction of current-year production. We developed unified models for the controls of ANPP through space and time. The relative importance of current-versus previous-year precipitation changes along a gradient of mean annual precipitation with the importance of current-year PPT decreasing, whereas the importance of previous-year PPT remains constant as mean annual precipitation increases. Finally, our results suggest that ANPP will respond to climate-change-driven alterations in water availability and, more importantly, that the magnitude of the response will increase with time.