The elemental composition of sediments in rivers is the product of physical and chemical erosion of rocks, which is then transported across drainage networks. A corollary is that fluvial sedimentary geochemistry can be used to understand geologic, climatic, and geomorphic processes. Here, we predict elemental compositions of river sediments using drainage networks extracted from digital elevation data and erosional models. The Geochemical Baseline Survey of the Environment was used to quantify substrate (i.e., source region) chemistry. Sedimentary compositions in rivers downstream are predicted by formally integrating eroding substrates with respect to distance downstream. Different erosional models, including the Stream Power model and uniform incision rates, are tested. Predictions are tested using a new suite of compositions obtained from fine grained (<150 μm) sediments at 67 sites along the Spey, Dee, Don, Deveron, and Tay rivers, Cairngorms, UK. Results show that sedimentary geochemistry can be predicted using simple models that include the topography of drainage networks and substrate compositions as input. The concentration of numerous elements including Magnesium, Rubidium, Uranium, Potassium, Calcium, Strontium, and Beryllium can be accurately predicted using this simple approach. Predictions are insensitive to the choice of erosional model, which we suggest is a consequence of broadly homogeneous rates of erosion throughout the study area. Principal component analysis of the river geochemical data suggests that the composition of most Cairngorms river sediments can be explained by mafic/felsic provenance and conservative mixing downstream. These results suggest that the elemental composition of river sediments can be accurately predicted using simple erosional models and digital elevation data.