Understanding changes in precipitation variability is essential for a complete explanation of the hydrologic cycle's response to warming and its impacts. While changes in mean and extreme precipitation have been studied intensively, precipitation variability has received less attention, despite its theoretical and practical importance. Here, we show that precipitation variability in most climate models increases over a majority of global land area in response to warming (66% of land has a robust increase in variability of seasonal-mean precipitation). Comparing recent decades to RCP8.5 projections for the end of the 21st century, we find that in the global, multi-model mean, precipitation variability increases 3-4% K-1 globally, 4-5% K-1 over land and 2-4% K-1 over ocean, and is remarkably robust on a range of timescales from daily to decadal. Precipitation variability increases by at least as much as mean precipitation and less than moisture and extreme precipitation for most models, regions, and timescales. We interpret this as being related to an increase in moisture which is partially mitigated by weakening circulation. We show that changes in observed daily variability in station data are consistent with increased variability.