Trade plays a key role in the spread of alien species and has arguably contributed to the recent enormous acceleration of biological invasions, thus homogenizing biotas worldwide. Combining data on 60‐year trends of bilateral trade, as well as on biodiversity and climate, we modeled the global spread of plant species among 147 countries. The model results were compared with a recently compiled unique global data set on numbers of naturalized alien vascular plant species representing the most comprehensive collection of naturalized plant distributions currently available. The model identifies major source regions, introduction routes, and hot spots of plant invasions that agree well with observed naturalized plant numbers. In contrast to common knowledge, we show that the ‘imperialist dogma,’ stating that Europe has been a net exporter of naturalized plants since colonial times, does not hold for the past 60 years, when more naturalized plants were being imported to than exported from Europe. Our results highlight that the current distribution of naturalized plants is best predicted by socioeconomic activities 20 years ago. We took advantage of the observed time lag and used trade developments until recent times to predict naturalized plant trajectories for the next two decades. This shows that particularly strong increases in naturalized plant numbers are expected in the next 20 years for emerging economies in megadiverse regions. The interaction with predicted future climate change will increase invasions in northern temperate countries and reduce them in tropical and (sub)tropical regions, yet not by enough to cancel out the trade‐related increase.