We synthesize geologic observations with new isotopic evidence for the timing and magnitude of uplift for the central Andes between 22°S and 26°S since the Paleocene. To estimate paleoelevations, we used the stable isotopic composition of carbonates and volcanic glass, combined with another paleoelevation indicator for the central Andes: the distribution of evaporites. Paleoelevation reconstruction using clumped isotope paleothermometry failed due to resetting during burial. The Andes at this latitude rose and broadened eastward in three stages during the Cenozoic. The first, in what is broadly termed the “Incaic” orogeny, ended by the late Eocene, when magmatism and deformation had elevated to ≥4 km the bulk (~50%) of what is now the western and central Andes. The second stage witnessed the gradual building of the easternmost Puna and Eastern Cordillera, starting with deformation as early as 38 Ma, to >3 km by no later than 15 Ma. The proximal portions of the Paleogene foreland basin system were incorporated into the orogenic edifice, and basins internal to the orogen were enclosed and isolated from easterly moisture sources, promoting the precipitation of evaporites. In the third orogenic stage during the Pliocene–Pleistocene, Andean deformation accelerated and stepped eastward to form the modern Subandes, accounting for the final ~15%–20% of the current cross section of the Andes. About 0.5 km of elevation was added unevenly to the Western Cordillera and Puna from 10 to 2 Ma by voluminous volcanism. The two largest episodes of uplift and eastward propagation of the orogenic front and of the foreland flexural wave, ca. 50 (?)–40 Ma and <5 Ma, overlap with or immediately postdate periods of very rapid plate convergence, high flux magmatism in the magmatic arc, and crustal thickening. Uplift does not correlate with a hypothesized mantle lithospheric foundering event in the early Oligocene. Development of hyperaridity in the Atacama Desert by the mid-Miocene postdates the two-step elevation gain to >3 km of most (~75%) of the Andes. Hence, the record suggests that hyperarid climate was a consequence, not major cause, of uplift through trench sediment starvation.