The Amazon basin hosts half the planet's remaining moist tropical forests, but they may be threatened in a warming world. Nevertheless, climate model predictions vary from rapid drying to modest wetting. Here we report that the catchment of the world's largest river is experiencing a substantial wetting trend since approximately 1990. This intensification of the hydrological cycle is concentrated overwhelmingly in the wet season driving progressively greater differences in Amazon peak and minimum flows. The onset of the trend coincides with the onset of an upward trend in tropical Atlantic sea surface temperatures (SST). This positive longer-term correlation contrasts with the short-term, negative response of basin-wide precipitation to positive anomalies in tropical North Atlantic SST, which are driven by temporary shifts in the intertropical convergence zone position. We propose that the Amazon precipitation changes since 1990 are instead related to increasing atmospheric water vapor import from the warming tropical Atlantic.