Groundwater, the largest available store of global freshwater, is relied upon by more than two billion people. It is therefore important to quantify the spatiotemporal interactions between groundwater and climate. However, current understanding of the global-scale sensitivity of groundwater systems to climate change—as well as the resulting variation in feedbacks from groundwater to the climate system—is limited. Here, using groundwater model results in combination with hydrologic data sets, we examine the dynamic timescales of groundwater system responses to climate change. We show that nearly half of global groundwater fluxes could equilibrate with recharge variations due to climate change on human (~100 year) timescales, and that areas where water tables are most sensitive to changes in recharge are also those that have the longest groundwater response times. In particular, groundwater fluxes in arid regions are shown to be less responsive to climate variability than in humid regions. Adaptation strategies must therefore account for the hydraulic memory of groundwater systems, which can buffer climate change impacts on water resources in many regions, but may also lead to a long, but initially hidden, legacy of anthropogenic and climatic impacts on river flows and groundwater-dependent ecosystems.