Wildfires burn large parts of the tropics every year, shaping ecosystem structure and functioning. Yet the complex interplay between climate, vegetation and human factors that drives fire dynamics is still poorly understood. Here we show that on all continents, except Australia, tropical fire regimes change drastically as mean annual precipitation falls below 550 mm. While the frequency of fires decreases below this threshold, the size and intensity of wildfires rise sharply. This transition to a regime of Rare-Intense-Big fires (RIB-fires) corresponds to the relative disappearance of trees from the landscape. Most dry regions on the globe are projected to become substantially drier under global warming. Our findings suggest a global zone where this drying may have important implications for fire risks to society and ecosystem functioning.