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Earth's forests, covering an area approximately Africa and Europe's landmasses combined, play a crucial role in mitigating climate change and sustaining global biodiversity. Climate change and land degradation will likely undermine forest integrity, as well as their role in climate mitigation, but little is known on where the greatest impacts may be. We integrate an assessment of contemporary forest integrity, which characterises the ecosystem's ability to adapt to anthropogenic impacts, and projections of future deforestation to present a comprehensive measure of global forest risk. We identify forests with exceptionally high isotherm shift velocities in the forests of east Europe, Boreal North America, and Amazonian South America. We show unmitigated land change is likely to amplify climate risk in more than a quarter of forests (29%), with notable risk across Central Africa, South Asia, and South America. However, notable differences in risks exist between different future scenarios, highlighting an opportunity to reduce risk by margins comparable to those required to meet the Paris Agreement's mitigation targets. Incorporating these results into strategic policy and management will support more sustainable use and protection of forest ecosystems and the services they provide.