The worldwide variation in vegetation height is fundamental to the global carbon cycle and central to the functioning of ecosystems and their biodiversity. Geospatially explicit and, ideally, highly resolved information is required to manage terrestrial ecosystems, mitigate climate change and prevent biodiversity loss. Here we present a comprehensive global canopy height map at 10 m ground sampling distance for the year 2020. We have developed a probabilistic deep learning model that fuses sparse height data from the Global Ecosystem Dynamics Investigation (GEDI) space-borne LiDAR mission with dense optical satellite images from Sentinel-2. This model retrieves canopy-top height from Sentinel-2 images anywhere on Earth and quantifies the uncertainty in these estimates. Our approach improves the retrieval of tall canopies with typically high carbon stocks. According to our map, only 5% of the global landmass is covered by trees taller than 30 m. Further, we find that only 34% of these tall canopies are located within protected areas. Thus, the approach can serve ongoing efforts in forest conservation and has the potential to foster advances in climate, carbon and biodiversity modelling.