Foreland basins record the regional isostatic compensation of mountain belts; during periods of crustal thickening, they subside, and when erosion unloads the mass of the mountains, the basins rebound and are eroded. In order to evaluate this mechanism for rebound, it is critical that the timing and magnitude of erosion are documented. We present data estimating the timing and magnitude of late orogenic or postorogenic erosion in the North Alpine Foreland Basin of Switzerland. Mineral cooling ages demonstrate that the basin underwent 1–3 km of erosion soon after 5 Ma. This erosion coincided with a decline in structural deformation in the Swiss Alps, and a doubling of sediment accumulation rates in surrounding depocenters. We propose that accelerated erosional unroofing of the Swiss Alps triggered isostatic rebound and erosion of the foreland basin after 5 Ma. A projection of the isostatic rebound of the basin into the mountains suggests that at least 6.5 km of erosion should have occurred in the high topography of the Aar Massif. Accelerated erosion in the Swiss Alps at that time is explained by an increase in atmospheric moisture driven by an intensification of the Atlantic Gulf Stream at 4.6 Ma. Consequently, we propose that the changing erosional capacity of the climate triggered late orogenic to postorogenic mass reduction and isostatic rebound of the Swiss Alps and their neighboring foreland basin.