The shear force along convergent plate boundary faults (megathrusts) determines the height of mountain ranges that can be mechanically sustained(1-4). However, whether the true height of mountain ranges corresponds to this tectonically supported elevation is debated(4-7). In particular, climate-dependent erosional processes are often assumed to exert a first-order control on mountain height(5-12), although this assumption has remained difficult to validate(12). Here we constrain the shear force along active megathrusts using their rheological properties and then determine the tectonically supported elevation using a force balance model. We show that the height of mountain ranges around the globe matches this elevation, irrespective of climatic conditions and the rate of erosion. This finding indicates that mountain ranges are close to force equilibrium and that their height is primarily controlled by the megathrust shear force. We conclude that temporal variations in mountain height reflect long-term changes in the force balance but are not indicative of a direct climate control on mountain elevation. Simulations using a force balance model match mountain heights observed around the globe, suggesting that mountain elevation is almost completely controlled by tectonic forces rather than erosion.