Accurate and scalable hydrologic models are essential building blocks of several important applications, from water resource management to timely flood warnings. However, as the climate changes, precipitation and rainfall-runoff pattern variations become more extreme, and accurate training data that can account for the resulting distributional shifts become more scarce. In this work we present a novel family of hydrologic models, called HydroNets, which leverages river network structure. HydroNets are deep neural network models designed to exploit both basin specific rainfall-runoff signals, and upstream network dynamics, which can lead to improved predictions at longer horizons. The injection of the river structure prior knowledge reduces sample complexity and allows for scalable and more accurate hydrologic modeling even with only a few years of data. We present an empirical study over two large basins in India that convincingly support the proposed model and its advantages.