Predictions of groundwater fluctuations in space and time are important for sustainable water resource management. Infiltration variability on monthly to decadal timescales leads to fluctuations in the water tables and thus groundwater resources. However, connections between global-scale climate variability and infiltration patterns and groundwater are often poorly understood because the relationships between groundwater conditions and infiltration tend to be highly nonlinear. In addition, understanding is further hampered because many groundwater records are incomplete and groundwater tables are often anthropogenically influenced, which makes identifying the effects of infiltration variability difficult. Previous studies that have evaluated how infiltration variability controls groundwater are based on a limited number of point measurements. Here, we present a global assessment of how infiltration variability is expected to affect groundwater tables. We use an analytical solution derived from Richards' equation to model water level responses to idealized periodic infiltration variability with periods that range from months to decades, to approximate both the effects of short-term and long-term climate variability and thus infiltration patterns. Our global-scale assessment reveals why infiltration variability would lead to periodicity in groundwater recharge in particular regions. The vadose zone strongly dampens short-term (seasonal and shorter) variations in infiltration fluxes throughout most of Earth's land surface, while infiltration cycles exceeding 1 year would yield transient recharge, except in more arid regions. Our results may help forecasting long-term groundwater tables and could support improving groundwater resource management.