Geographic gradients in the species richness of non-human primates have traditionally been attributed to the variation in forest productivity (related to precipitation levels), although an all-inclusive, global-scale analysis has never been conducted. We perform a more comprehensive test on the role of precipitation and biomass production and propose an alternative hypothesis - the variation in vertical structure of forest habitats as measured by forest canopy height - in determining primate species richness on a global scale. Considering the potential causal relationships among precipitation, productivity and forest structure, we arranged these variables within a path framework to assess their direct and indirect associations with the pattern of primate species richness using structural equation modelling. The analysis also accounted for the influence of spatial autocorrelation in the relationships and assessed possible historical differences among biogeographical regions. The path coefficients indicate that forest canopy height (used as a proxy for vertical forest structure) is a better predictor of primate species richness than either precipitation or productivity on both global and continental scales. The only exception was Asia, where precipitation prevailed, albeit independently from productivity or forest structure. The influence of spatially structured processes varied markedly among biogeographical regions. Our results challenge the traditional rainfall-based viewpoint in favour of forest distribution and structure as primary drivers of primate species richness, which aggregate potential effects from both climatic factors and habitat complexity. These findings may support predictions of the impact of forest removal on primate species richness.