Humans have moved species away from their native ranges since the Neolithic, but globalization accelerated the rate at which species are being moved. We fitted more than half million distribution models for 610 traded bird species on the CITES list to examine the separate and joint effects of global climate and land-cover change on their potential end-of-century distributions. We found that climate-induced suitability for modelled invasive species increases with latitude, because traded birds are mainly of tropical origin and much of the temperate region is ‘tropicalizing.’ Conversely, the tropics are becoming more arid, thus limiting the potential from cross-continental invasion by tropical species. This trend is compounded by forest loss around the tropics since most traded birds are forest dwellers. In contrast, net gains in forest area across the temperate region could compound climate change effects and increase the potential for colonization of low-latitude birds. Climate change has always led to regional redistributions of species, but the combination of human transportation, climate, and land-cover changes will likely accelerate the redistribution of species globally, increasing chances of alien species successfully invading non-native lands. Such process of biodiversity homogenization can lead to emergence of non-analogue communities with unknown environmental and socioeconomic consequences.