The deepest valleys of the Andes have been cut in southern Peru by the Ríos Cotahuasi Ocoña and Colca–Majes. These canyons are Late Miocene landforms based on a new ignimbrite stratigraphy supported by 42 new 40Ar/39Ar age determinations obtained on plateau-forming and valley-filling ignimbrites. Between 19 and 13 Ma, a gently sloping surface bevelling the clastic wedge southeast of the developing mountain front was mantled by widespread ignimbrites. After 13 Ma, this paleosurface was tilted up from 2.2 km a.s.l. at the mountain front to 4.3 km a.s.l. at the base of the Pliocene and Pleistocene volcanoes that crown the southwestern edge of the Altiplano. The canyons incised this topography after 9 Ma, while the dated base of younger ignimbrite valley fills suggests that these canyons had been cut down to near their present depths as early as 3.8 Ma. By 1.4 Ma, however, the canyons had been almost completely refilled by 1.3 km-thick unwelded pyroclastic deposits, which were subsequently eroded. Valley incision since 9 Ma at an average rate of 0.2 mm yr−1 is the response to topographic uplift after 13 Ma combined with increasing runoff due to a wetter climate recorded after 7 Ma. Although long-term aridity generated an imbalance between high long-term uplift rates and low plateau denudation rates, the combination of aridity and volcanism still promoted canyon incision because episodic volcanic fills maintained a cycle of catastrophic debris avalanches and subsequent dam breakouts.