Both theory and evidence suggest that diversity stabilises productivity in herbaceous plant communities through a combination of overyielding, species asynchrony and favourable species interactions. However, whether these same processes also promote stability in forest ecosystems has never been tested. Using tree ring data from permanent forest plots across Europe, we show that aboveground wood production is inherently more stable through time in mixed-species forests. Faster rates of wood production (i.e. overyielding), decreased year-to-year variation in productivity through asynchronous responses of species to climate, and greater temporal stability in the growth rates of individual tree species all contributed strongly to stabilising productivity in mixed stands. Together, these findings reveal the central role of diversity in stabilising productivity in forests, and bring us closer to understanding the processes which enable diverse forests to remain productive under a wide range of environmental conditions.