Abstract Biological communities are reshuffling owing to species range shifts in response to climate change. This process inherently leads to novel assemblages of interacting species. Yet, how climatic change and local dynamics in biotic interactions jointly affect range shifts is still poorly understood. We combine a unique long‐term transplant competition‐exclusion experiment with species distribution models (SDMs) to test the effects of biotic interactions on understorey species range shifts under climate change in European temperate forests. Using a time series of 18 years of individual‐level demographic data of four common understorey plant species transplanted beyond their cold range edge to plots with and without interspecific competition, we built integral projection models (IPMs) and analysed the effects of competition on five key vital rates and population growth (λ). We assessed the results of the transplant experiment in the context of the modelled species' current and future potential distributions. We find that species' population performances in the transplant experiment decreased with lower predicted habitat suitability from the SDMs. The population performance at the transplant sites was mediated by biotic interactions with the local plant community: for two species with intermediate levels of predicted habitat suitability at the transplant sites, competition effects could explicitly differentiate between net population growth (λ > 1) or shrinkage (λ < 1). Synthesis. Our findings contest the long‐standing idea that at cold range edges, mainly abiotic factors structure species' distributions. We conclude that biotic interactions, through acting on local population dynamics, may impact species distributions at the continental scale. Hence, predicting climate‐change impacts on biodiversity redistributions ultimately requires us to also integrate dynamics in biotic interactions.