AbstractGroundwater response to climate variations is often pivotal to managing groundwater sustainably. However, this relationship is rarely explicitly examined because of the complexity of surface to subsurface processes and the diverse impacts of multiple drivers, such as groundwater pumping and land use changes. In this paper, we address this challenge by proposing methods to quantify the sensitivity of groundwater level and recharge to temporal climate variability across Australia. Using the HydroSight groundwater hydrograph toolbox we first identify 1,143 out of a total of 4,350 bores as climate‐driven, where historically, head was primarily driven by climate variations. Streamflow elasticity measures are then adapted to groundwater to quantify the long‐term head and recharge sensitivity. We find that the national median sensitivity of head and recharge to precipitation change are 42 and 0.43 mm mm−1, respectively (interquartiles: 20–77 and 0.30–0.55 mm mm−1); both of which are ∼8 times that of potential evapotranspiration. Nationally, the results are spatially correlated, suggestive of large‐scale effects. The responses of head and recharge appear to be primarily related to climate type and hydrogeology. The more arid the climate, the higher the head sensitivity but the lower the recharge sensitivity. Porous media generally show higher head sensitivity than fractured media due to smaller aquifer specific yield, and again contrarily for that of recharge. These findings contribute to understanding the long‐term impact of climate change on groundwater and thus provide valuable insights for sustainable groundwater management.