Rapid expansion (RE) of tropical cyclones (TCs) is a structural evolution that specifies the dramatic geometric synthesis increase in TC size. Its destructive potential is comparable or even more pronounced than that by the TC rapid intensification but receives limited attention. In this study, we utilise the ERA5‐derived 41‐year (1979–2019) global climatology of TC outer size data (i.e., effective azimuthal‐area‐average radius of 34‐kt gale‐force surface winds, R34EFF) to define RE and reveal the global climatology of RE for the first time, where RE is defined as the 90th percentile of global expanding samples (i.e., ΔR34EFF > 50 NM per 24 h; 1 NM = 1.852 km). Statistics show that 32% of all TCs underwent RE at least once during their lifetime. Climatologically, the proportion of RE decreased significantly in the globe (7%) and Northern Hemisphere (9%), particularly in the western North Pacific (8%). Seasonally, the RE proportion peaks in the early and late TC seasons. Spatiotemporally, distinct spatiotemporal variations and interdecadal changes of RE are found. In view of TC lifecycle, TCs likely reach their lifetime maximum intensity and lifetime maximum size after RE initiation. The duration of RE varies widely from basin to basin, while its seasonal variability is relatively smaller. Regarding the relationship between RE and TC intensity, the intensity of rapidly expanding TCs may increase or decrease with the former being more likely. The initial size and intensity of rapidly expanding TCs tend to be small (45 NM) and weak (60 kt), respectively. This study advances the understanding of RE from a global perspective, laying important groundwork for future study.