Vegetation affects precipitation patterns by mediating moisture, energy and trace-gas fluxes between the surface and atmosphere. When forests are replaced by pasture or crops, evapotranspiration of moisture from soil and vegetation is often diminished, leading to reduced atmospheric humidity and potentially suppressing precipitation. Climate models predict that large-scale tropical deforestation causes reduced regional precipitation, although the magnitude of the effect is model and resolution dependent. In contrast, observational studies have linked deforestation to increased precipitation locally but have been unable to explore the impact of large-scale deforestation. Here we use satellite remote-sensing data of tropical precipitation and vegetation, combined with simulated atmospheric transport patterns, to assess the pan-tropical effect of forests on tropical rainfall. We find that for more than 60 per cent of the tropical land surface (latitudes 30 degrees south to 30 degrees north), air that has passed over extensive vegetation in the preceding few days produces at least twice as much rain as air that has passed over little vegetation. We demonstrate that this empirical correlation is consistent with evapotranspiration maintaining atmospheric moisture in air that passes over extensive vegetation. We combine these empirical relationships with current trends of Amazonian deforestation to estimate reductions of 12 and 21 per cent in wet-season and dry-season precipitation respectively across the Amazon basin by 2050, due to less-efficient moisture recycling. Our observation-based results complement similar estimates from climate models, in which the physical mechanisms and feedbacks at work could be explored in more detail.