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Exchange of solutes and particles between river channels and the subsurface is critical for biogeochemical processes in rivers. Subsurface water moves slowly, delaying downstream transport and providing ample time for reactions to proceed. We present a stochastic modeling framework for the transport of reactive solutes in rivers based on continuous time random walk theory. This model includes solute transport, storage, and reactions in both the channel and the bed. Hyporheic residence times can take any distribution. The model produces realistic breakthrough curves for conservative and reactive solutes. Reactive solutes breakthrough curves exhibit characteristic late time truncation. We have also extended the model for river networks and use it to assess how the interaction of exchange rates, residence time distributions and reaction rates affect export at the watershed scale. We show that extended travel …