Increasing global precipitation has been associated with a warming climate resulting from a strengthening of the hydrological cycle. This increase, however, is not spatially uniform. Observations and models have found that changes in rainfall show patterns characterized as wet-gets-wetter and warmer-gets-wetter. These changes in precipitation are largely located in the tropics and hence are probably associated with convection. However, the underlying physical processes for the observed changes are not entirely clear. Here we show from observations that most of the regional increase in tropical precipitation is associated with changes in the frequency of organized deep convection. By assessing the contributions of various convective regimes to precipitation, we find that the spatial patterns of change in the frequency of organized deep convection are strongly correlated with observed change in rainfall, both positive and negative (correlation of 0.69), and can explain most of the patterns of increase in rainfall. In contrast, changes in less organized forms of deep convection or changes in precipitation within organized deep convection contribute less to changes in precipitation. Our results identify organized deep convection as the link between changes in rainfall and in the dynamics of the tropical atmosphere, thus providing a framework for obtaining a better understanding of changes in rainfall. Given the lack of a distinction between the different degrees of organization of convection in climate models, our results highlight an area of priority for future climate model development in order to achieve accurate rainfall projections in a warming climate.