The Meridiani Planum region of Mars has been identified as a region of past aqueous activity by a combination of orbital and in situ observations that revealed evidence for sulfate-rich dirty evaporites formed in a playa setting. We investigate the hydrology and sedimentary record of this area using global and regional hydrological models in which groundwater flow is driven by a combination of precipitation, evaporation, and the surface topography. Groundwater evaporation results in evaporite precipitation and cementation of aeolian sediments, allowing the accumulation of deposits of substantial thickness, which then affect the subsequent patterns of groundwater flow. Hydrological activity is initially predicted to be isolated to the deepest craters and depressions, primarily within the Arabia Terra region surrounding Meridiani. As these depressions fill with sediments, the groundwater upwelling spreads laterally across broad regions of Arabia Terra, including Meridiani Planum, as well as regional topographic lows such as the northern lowlands and large impact basins. The model predictions are borne out by observations of large intracrater deposits, inverted valley networks, finely layered deposits, spectral evidence for hydrated sulfates, and pedestal craters that preserve the remnants of a much larger deposit that once covered much of Arabia Terra. The results suggest that the inferred playa at Meridiani was part of a regionally extensive zone of groundwater upwelling. This hydrological cycle requires that conditions in the late Noachian to early Hesperian must have been conducive to the existence of liquid water at the surface throughout much of the low latitudes of Mars.