Although the structural geometry of the Cenozoic Altiplano-Puna plateau in the central Andes is well defined, the temporal evolution of this contractile deformation is poorly constrained. To address this shortcoming, we used apatite fission track thermochronology (AFT) to quantify the cooling and exhumation history along a transect at 21¿S in southern Bolivia, through the deformed intermontane Altiplano basin, the doubly vergent thrust belt of the Eastern Cordillera and the inner foreland thrust belt east of the plateau (Interandean Zone). Thermal history modeling combined with published balanced cross sections and stratigraphic data constrain exhumation histories. Exhumation started during the late Eocene (40--36 Ma) in the central Eastern Cordillera, possibly due to bivergent thrusting and Cretaceous rift structure inversion. During the early Oligocene (33--27 Ma), exhumation spread across the study area as the current boundary thrusts of the Eastern Cordillera were activated. The inner west vergent thrust system became active in irregular order until circa 20 Ma, whereas the east vergent Interandean thrust belt formed by eastward propagating deformation since circa 30 Ma. Plateau exhumation continued at ~0.2 mm/yr until shortening terminated by 11--7 Ma. Shortening within the plateau since circa 30 Ma did not evolve by lateral accretion of thrust wedges; the propagating deformation style is spatially confined to the foreland thrust belt, which initiated coeval to plateau deformation (Interandean Zone) but propagated mainly after circa 10 Ma (Subandean Zone). Early Oligocene plateau-wide tectonically driven exhumation suggests that subduction-related processes had already thermally weakened the continental lithosphere prior to the 27--25 Ma onset of volcanic activity.