Rivers are a major component of sediment routing systems that control the transfer of terrigenous sediments from source to sink. Although it is widely accepted that rivers are perturbed by millennial-scale climatic variability, the extent to which these signals are buffered or transferred down river systems to be recorded in sediments at or beyond the river mouth remains debated. Here, we employ a physically based numerical model to address this outstanding issue. Our model shows that river transport strongly amplifies high-frequency sediment flux variations arising from changing water discharge, due to positive feedback between discharge and the channel gradient. This behavior is distinctly different from short-period sediment flux signals (with constant water discharge) where the output sediment flux is strongly dampened within the river, due to negative feedback between the channel gradient and sediment concentration. We conclude that marine sedimentary basins may record sediment flux cycles resulting from discharge (and ultimately climate) variability, whereas they may be relatively insensitive to pure sediment flux perturbations (such as for example those induced by tectonics).