The rates of anthropogenic climate change substantially exceed those at which forest ecosystems – dominated by immobile, long-lived organisms – are able to adapt. The resulting maladaptation of forests has potentially detrimental effects on ecosystem functioning. Furthermore, as many forest-dwelling species are highly dependent on the prevailing tree species, a delayed response of the latter to a changing climate can contribute to an extinction debt and mask climate-induced biodiversity loss. However, climate change will likely also intensify forest disturbances. Here, we tested the hypothesis that disturbances foster the reorganization of ecosystems and catalyze the adaptation of forest composition to climate change. Our specific objectives were (i) to quantify the rate of autonomous forest adaptation to climate change, (ii) examine the role of disturbance in the adaptation process, and (iii) investigate spatial differences in climate-induced species turnover in an unmanaged mountain forest landscape (Kalkalpen National Park, Austria). Simulations with a process-based forest landscape model were performed for 36 unique combinations of climate and disturbance scenarios over 1000 years. We found that climate change strongly favored European beech and oak species (currently prevailing in mid- to low-elevation areas), with novel species associations emerging on the landscape. Yet, it took between 357 and 706 years before the landscape attained a dynamic equilibrium with the climate system. Disturbances generally catalyzed adaptation and decreased the time needed to attain equilibrium by up to 211 years. However, while increasing disturbance frequency and severity accelerated adaptation, increasing disturbance size had the opposite effect. Spatial analyses suggest that particularly the lowest and highest elevation areas will be hotspots of future species change. We conclude that the growing maladaptation of forests to climate and the long lead times of autonomous adaptation need to be considered more explicitly in the ongoing efforts to safeguard biodiversity and ecosystem services provisioning.