Our understanding of how climate influences species distributions and our ability to assess the risk of introduced species depend on the assumption that species' climatic niches remain stable across space and time. While niche shifts have been detected in individual invasive species, one assessment of ~50 plants in Europe and North America concluded that niche shifts were rare, while another concluded the opposite. These contradictory findings, limited in species number and geographic scope, leave open a need to understand how often introduced species experience niche shifts and whether niche shifts can be predicted. We found evidence of climatic niche shifts in 65-100% of 815 terrestrial plant species introduced across five continents, depending on how niche shifts were measured. Individual species responses were idiosyncratic, but we generally saw that niche shifts reflected changes in climate availability at the continent scale and were largest in long-lived and cultivated species. Smaller intercontinental niche shifts occurred within species' native ranges. Overall, the climatic niches of terrestrial plant species were not conserved as they crossed continents. These results have major consequences for applying environmental niche models to assess the risk of invasive species and for predicting species responses to climate change. Our findings challenge the tenet that species' niches are conserved aspects of their ecology.