Ecological niche models have been instrumental in understanding and forecasting the widespread shifts in species distributions under global change. However, growing evidence of evolution in spreading populations challenges their key assumption of niche conservatism, limiting model transferability in space and time. Climate niche evolution has been studied extensively in invasive species, but may also occur in native populations tracking climate change, when species encounter novel abiotic conditions that vary with latitude. We compared niche shifts during native range expansion and during invasion in Dittrichia graveolens, a Mediterranean annual plant species that is currently undergoing both types of spread. We asked whether the species' northward native range expansion in Eurasia matched climate change from 1901-1930 to 1990-2019, or if further range expansion was promoted by niche evolution. In addition, we asked how niche expansion in the native range affected forecasts of two ongoing invasions in Australia and California. We quantified niche shifts in environmental space using the analytical framework of niche centroid shift, overlap, unfilling, and expansion (COUE), and examined associated distribution changes in geographic space using Maximum Entropy modeling. Our results show that D. graveolens expanded its native range well beyond what would be sufficient to track climate change, a shift associated with a 5.5% niche expansion to include more temperate climates. In contrast, both invasions showed evidence of niche conservatism, with niche filling depending on invader residence time. Including the expanded native niche in invasion projections added new areas at risk of invasion, but none of these has been colonized at present. We conclude that native populations may track climate change and adapt to novel local conditions in parallel, causing an evolutionary expansion of the climate niche and more widespread range expansion than expected based on climate change alone.