The denudation rate signal of the Bolivian Andes as measured by cosmogenic 10Be in sediment is preserved in the floodplain of adjacent foreland basins even though these basins store the sediment for thousands of years. This conclusion is drawn from comparing published Andean source area denudation rates with new cosmogenic 10Be data as measured in the floodplains of the large Beni and Mamoré basins. For the entire Beni basin including the sediment-producing Andes and the vast flooded plains of the foreland, the cosmogenic nuclide-derived denudation rate is 0.45 ± 0.06 mm/yr, while that of the Mamoré basin is 0.55 ± 0.19 mm/yr. By comparison, the respective Andean source areas erode at averaged rates of 0.37 ± 0.06 mm/yr (upper Beni), and at 0.56 ± 0.09 mm/yr (upper Mamoré). We notice a decrease in variability of denudation rate with increasing spatial scale as small-scale processes are averaged out. Sediment mixing within the floodplain damps scatter of nuclide-derived denudation rates picked up in the source area. On the temporal scale, a remarkable agreement between cosmogenic nuclide-derived rates averaging over a few kiloyears with those from fission track dating averaging over millions of years seems to suggest that cosmogenic nuclide-derived denudation rates capture the long-term erosional characteristics of the mountain belt. The sum of these observations suggests that any sample collected along a river traversing a floodplain will yield the denudation rate of the source area. This finding opens the unique possibility of constraining cosmogenic nuclide-derived paleo-sediment budgets for these large basins as the long-term, spatially-averaged denudation rate signal of the sediment-producing area is preserved in sedimentary archives.