Canopy structure, defined by leaf area index (LAI), fractional vegetation cover (FCover) and fraction of absorbed photosynthetically active radiation (fAPAR), regulates a wide range of forest functions and ecosystem services. Spatially consistent field-measurements of canopy structure are however lacking, particularly for the tropics. Here, we introduce the Global LAI database: a global dataset of field-based canopy structure measurements spanning tropical forests in four continents (Africa, Asia, Australia and the Americas). We use these measurements to test for climate dependencies within and across continents, and to test for the potential of anthropogenic disturbance and forest protection to modulate those dependences. Using data collected from 887 tropical forest plots, we show that maximum water deficit, defined across the most arid months of the year, is an important predictor of canopy structure, with all three canopy attributes declining significantly with increasing water deficit. Canopy attributes also increase with minimum temperature, and with the protection of forests according to both active (within protected areas) and passive measures (through topography). Once protection and continent effects are accounted for, other anthropogenic measures (e.g. human population) do not improve the model. We conclude that canopy structure in the tropics is primarily a consequence of forest adaptation to the maximum water deficits historically experienced within a given region. Climate change, and in particular changes in drought regimes may thus affect forest structure and function, but forest protection may offer some resilience against this effect.