Active graben systems in south Tibet and the Himalaya are the surface expression of ongoing E-W extension, however, the cause and spatio-temporal evolution of normal faulting remain debated. Here, we reconstruct the exhumation history driven by normal faulting at the southern Tangra Yumco graben using new thermochronological data. The Miocene cooling history of the footwall of the main graben-bounding fault is constrained by zircon (U-Th)/He ages (16.7±1.0 to 13.3±0.6 Ma), apatite fission track ages (15.9±2.1 to 13.0±2.1 Ma), and apatite (U-Th)/He ages (7.9±0.4 to 5.3±0.3 Ma). Thermo-kinematic modelling of the data indicates that normal faulting began 19.0±1.1 Ma ago at a rate of ∼0.2 km/Myr and accelerated to ∼0.4 km/Myr at ∼5 Ma. In the northern Tangra Yumco rift, re-modelling of published data shows that faulting started ∼5 Ma later at 13.9±0.8 Ma. The age difference and the distance of 130 km between the two sites indicates that rifting and normal faulting propagated northward at an average rate of ∼25 km/Myr. As this rate is similar to the Miocene convergence rate between India and south Tibet, we argue that the underthrusting of India beneath Tibet has exerted an important control on the propagation of rifts in south Tibet.