Changes in Earth's surface elevation can be linked to the geodynamic processes that drive surface uplift, which in turn modulate regional climate patterns. We document hydrogen isotopic compositions of hydrated volcanic glasses and modern stream waters to determine late Cenozoic surface uplift across the Peruvian central Andes. Modern water isotopic compositions reproduce mean catchment elevations to a precision better than ±500 m (1σ). Glass isotopic data show a spatiotemporally variable transition from isotopically heavy to isotopically light compositions. The latter are consistent with modern water on the plateau. When interpreted in the context of published paleoelevation estimates and independent geological information, the isotopic data indicate that elevation rapidly increased by 2-2.5 km from 20-17 Ma in the central Western Cordillera, and from 15-10 Ma in the southern Western Cordillera and Altiplano; these patterns are consistent with foundering of mantle lithosphere via Rayleigh-Taylor instability. The Eastern Cordillera was slowly elevated 1.5-2 km between 25 and 10 Ma, a rate consistent with crustal shortening as the dominant driver of surface uplift. The Ayacucho region attained modern elevation by ~22 Ma. The timing of orographic development across southern Peru is consistent with the early Miocene onset and middle Miocene intensification of hyperarid conditions along the central Andean Pacific coast.