In many regions, tectonic uplift is the main driver of erosion over million-year (Myr) timescales, but climate changes can markedly affect the link between tectonics and erosion, causing transient variations in erosion rates. Here we study the driving forces of millennial to Myr-scale erosion rates in the French Western Alps, as estimated from in situ produced cosmogenic 10Be and a newly developed approach integrating detrital and bedrock apatite fission-track thermochronology. Millennial erosion rates from 10Be analyses vary between ~0.27 and ~1.33 m/kyr, similar to rates measured in adjacent areas of the Alps. Significant positive correlations of millennial erosion rates with geomorphic measures, in particular with the LGM ice thickness, reveal a strong transient morphological and erosional perturbation caused by repeated Quaternary glaciations. The perturbation appears independent of Myr-scale uplift and erosion gradients, with the effect that millennial erosion rates exceed Myr-scale erosion rates only in the internal Alps where the latter are low (<0.4 km/Myr). These areas, moreover, exhibit channels that clearly plot above a general linear positive relation between Myr-scale erosion rates and normalized steepness index. Glacial erosion acts irrespective of rock uplift and thus not only leads to an overall increase in erosion rates but also regulates landscape morphology and erosion rates in regions with considerable spatial gradients in Myr-scale tectonic uplift. Our study demonstrates that climate change, e.g., through occurrence of major glaciations, can markedly perturb landscape morphology and related millennial erosion rate patterns, even in regions where Myr-scale erosion rates are dominantly controlled by tectonics.