Solute transport in rivers is controlled by surface hydrodynamics and by mass exchanges between the surface stream and distinct retention zones. This paper presents a residence time model for stream transport of solutes, Solute Transport in Rivers (STIR), that accounts for the effect of the stream-subsurface interactions on river mixing. A stochastic approach is used to derive a relation between the in-stream solute concentration and the residence time distributions (RTDs) in different retention domains. Particular forms of the RTD are suggested for the temporary storage within surface dead zones and for bed form–induced hyporheic exchange. This approach is advantageous for at least two reasons. The first advantage is that exchange parameters can generally be expressed as functions of physical quantities that can be reasonably estimated or directly measured. This gives the model predictive capabilities, and the results can be generalized to conditions different from those directly observed in field experiments. The second reason is that individual exchange processes are represented separately by appropriate residence time distributions, making the model flexible and modular, capable of incorporating the effects of a variety of exchange processes and chemical reactions in a detailed way. The capability of the model is illustrated with an example and with an application to a field case. Analogies and differences with other established models are also discussed.