Abstract Niche conservatism, i.e. the retention of a species’ fundamental niche through evolutionary time, is cornerstone for biological invasion assessments. The fact that species tend to maintain their original climate niche allows predictive maps of invasion risk to anticipate potential invadable areas. Unravelling the mechanisms driving niche shifts can shed light on the management of invasive species. Here, we assessed niche shifts in one of the world's worst invasive species: the wild boar Sus scrofa. We also predicted potential invadable areas based on an ensemble of three ecological niche modelling methods, and evaluated the performance of models calibrated with native vs. pooled (native plus invaded) species records. By disentangling the drivers of change on the exotic wild boar population's niches, we found strong evidence for niche conservatism during biological invasion. Ecological niche models calibrated with both native and pooled range records predicted convergent areas. Also, observed niche shifts are mostly explained by niche unfilling, i.e. there are unoccupied areas in the exotic range where climate is analogous to the native range. Niche unfilling is expected as result of recent colonization and ongoing dispersal, and was potentially stronger for the Neotropics, where a recent wave of introductions for pig‐farming and game‐hunting has led to high wild boar population growth rates. The invasive potential of wild boar in the Neotropics is probably higher than in other regions, which has profound management implications if we are to prevent their invasion into species‐rich areas, such as Amazonia, coupled with expansion of African swine fever and possibly great economic losses. Although the originally Eurasian‐wide distribution suggests a pre‐adaptation to a wide array of climates, the wild boar world‐wide invasion does not exhibit evidence of niche evolution. The invasive potential of the wild boar therefore probably lies on the reproductive, dietary and morphological characteristics of this species, coupled with behavioural thermoregulation.