Recent acceleration of sand extraction for anthropic use threatens the sustainability of this major resource. However, continental erosion and river transport, which produce sand and sediment in general, lack quantification at the global scale. Here, we develop a new geodetic method to infer the sediment discharge to ocean of the world's largest rivers. It combines the spatial distribution of modern sedimentation zones with new high-resolution (~170 km) data from the Gravity Recovery and Climate Experiment (GRACE) mission launched in 2002. We obtain sediment discharges consistent with in situ measurements for the Amazon, Ganges-Brahmaputra, Changjiang, Indus, and Magdalena rivers. This new approach enables to quantitatively monitor the contemporary erosion of continental basins drained by rivers with large sediment discharges and paves the way toward a better understanding of how natural and anthropic changes influence landscape dynamics.