During the last two centuries, thousands of insect species have been transported (largely inadvertently) and established outside of their native ranges worldwide, some with catastrophic ecological and economic impacts. Global variation in numbers of invading species depends on geographic variation in propagule pressure and heterogeneity of environmental resistance to invasions. Elton’s diversity-invasibility hypothesis, proposed over sixty years ago, has been widely explored for plants but little is known on how biodiversity affects insect invasions. Here we use species inventories from 44 land areas, ranging from small oceanic islands to entire continents in various world regions, to show that numbers of established insect species are primarily driven by diversity of plants, with both native and non-native plant species richness being the strongest predictor of insect invasions. We find that at large spatial scales, plant diversity directly explains variation in non-native insect species richness among world regions, while geographic factors such as land area, climate and insularity largely affect insect invasions indirectly via their effects on local plant richness.