Significance: Tropical cyclones (TCs), and particularly major TCs, pose substantial risk to many regions around the globe. Identifying changes in this risk and determining causal factors for the changes is a critical element for taking steps toward adaptation. Theory and numerical models consistently link increasing TC intensity to a warming world, but confidence in this link is compromised by difficulties in detecting significant intensity trends in observations. These difficulties are largely caused by known heterogeneities in the past instrumental records of TCs. Here we address and reduce these heterogeneities and identify significant global trends in TC intensity over the past four decades. The results should serve to increase confidence in projections of increased TC intensity under continued warming.