Fast uplift and exhumation of the Himalaya and Tibet and fast subsidence in the foreland basin portray the primary Neogene evolution of the Indian-Eurasian collision zone. We relate these events to the relative northward drift of India over its own slab. Our mantle-flow model derived from seismic tomography shows that dynamic topography over the southward-folded Indian slab explains the modern location of the foreland depocenter. Back in time, our model suggests that the stretched Indian slab detached from the Indian plate during the indentation of the Eurasian plate, and remained stationary underneath the northward-drifting Indian continent. We model the associated southward migration of the dynamic deflection of the topography and show that subsidence has amounted to ∼6000 m in the foreland basin since 15 Ma, while the dynamic surface uplift of the Himalaya amounted to ∼1000 m during the early Miocene. While competing with other processes, transient dynamic topography may thus explain, to a large extent, both the uplift history of the Himalaya and subsidence of its foreland basin, and should not be ignored.