The uplift of the Tibetan plateau is generally regarded as a response to the convective removal of the lower portion of the thickened Asian lithosphere. This removal is also thought to be responsible for the east- west extension that took place during the India-Asia collision. The timing of these events has been a subject of great interest for understanding mountain- building processes, collisional tectonics and the influence of these processes on climate change. In western Tibet, potassic lavas related to east-west extension were found to have been extruded over the past 20 Myr (refs 5, 6). Here we report the widespread occurrence of magmas in eastern Tibet which show similar geochemical signatures to the potassic lavas to the west but formed 40-3- Myr ago. These magmatic activities suggest a diachronous uplift history for the Tibetan plateau, with the convective removal of the lower lithosphere inducing rapid uplift in the east beginning some 40 Myr ago and in the west about 20 Myr later. This observation is consistent with sedimentation records from the Ganges-Brahmaputra delta to the Bengal fan and can better account for the tectonically driven models for strontium isotope evolution in the ocean and global cooling over the past 40 Myr.