Future climate simulations feature pronounced spatial shifts in the structure of tropical rainfall. We apply a novel atmospheric energy flux analysis to diagnose late 21st century tropical rainfall shifts in a large ensemble of simulations of 21st century climate. The method reconstructs 2D spatial changes in rainfall based on horizontal shifts in the lines of zero meridional and zonal divergent energy flux, called the energy flux equator (EFE) and energy flux prime meridian (EFPM), respectively. Two main sources of future atmospheric energy flux changes, and hence rainfall shifts, are identified by the analysis: the high-latitude North Atlantic due to a weakened Atlantic Meridional Overturning Circulation that shifts tropical rainfall southwards over the greater Tropical Atlantic sector and eastern Pacific; and the eastern tropical Pacific due to a permanent El-Nino-like response that produces zonal shifts over the Maritime Continent and South America. To first order, the shifts in the EFE and EFPM mirror gross distributional changes in tropical precipitation, with a southward shift in rainfall over the tropical Atlantic, West Africa, and eastern tropical Pacific and an eastward shift over the Maritime Continent and western Pacific. When used to reconstruct future rainfall shifts in the tropical Atlantic and Sahel, the method reasonably represents the simulated meridional structure of rainfall shifts but does not do so for the zonal structures.