Nations have committed to ambitious conservation targets in response to accelerating rates of global biodiversity loss. Anticipating future impacts is essential to inform policy decisions for achieving these targets, but predictions need to be of sufficiently high spatial resolution to forecast the local effects of global change. As part of the intercomparison of biodiversity and ecosystem services models of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services, we present a fine-resolution assessment of trends in the persistence of global plant biodiversity. We coupled generalized dissimilarity models, fitted to >52 million records of >254 thousand plant species, with the species-area relationship, to estimate the effect of land-use and climate change on global biodiversity persistence. We estimated that the number of plant species committed to extinction over the long term has increased by 60% globally between 1900 and 2015 (from ~10,000 to ~16,000). This number is projected to decrease slightly by 2050 under the most optimistic scenario of land-use change and to substantially increase (to ~18,000) under the most pessimistic scenario. This means that, in the absence of climate change, scenarios of sustainable socio-economic development can potentially bring extinction risk back to pre-2000 levels. Alarmingly, under all scenarios, the additional impact from climate change might largely surpass that of land-use change. In this case, the estimated number of species committed to extinction increases by 3.7-4.5 times compared to land-use-only projections. African regions (especially central and southern) are expected to suffer some of the highest impacts into the future, while biodiversity decline in Southeast Asia (which has previously been among the highest globally) is projected to slow down. Our results suggest that environmentally sustainable land-use planning alone might not be sufficient to prevent potentially dramatic biodiversity loss, unless a stabilization of climate to pre-industrial times is observed.