Climate influences the erosion processes acting at the Earth's surface. However, the effect of cooling during the Late Cenozoic era, including the onset of Pliocene-Pleistocene Northern Hemisphere glaciation (about two to three million years ago), on global erosion rates remains unclear. The uncertainty arises mainly from a lack of consensus on the use of the sedimentary record as a proxy for erosion and the difficulty of isolating the respective contributions of tectonics and climate to erosion. Here we compile 18,000 bedrock thermochronometric ages from around the world and use a formal inversion procedure to estimate temporal and spatial variations in erosion rates. This allows for the quantification of erosion for the source areas that ultimately produce the sediment record on a timescale of millions of years. We find that mountain erosion rates have increased since about six million years ago and most rapidly since two million years ago. The increase of erosion rates is observed at all latitudes, but is most pronounced in glaciated mountain ranges, indicating that glacial processes played an important part. Because mountains represent a considerable fraction of the global production of sediments, our results imply an increase in sediment flux at a global scale that coincides closely with enhanced cooling during the Pliocene and Pleistocene epochs.