Hyporheic flows, which stem from the interaction between stream flow and bedform, transport solute-laden surface waters into the streambed sediments, where reactive solutes undergo biogeochemical transformations. Despite the importance of hyporheic exchange on riverine ecosystem and biogeochemical cycles, research is limited on the effects of hyporheic fluxes on the fate of reactive solutes within the hyporheic zone. Consequently, we investigate the controls of hyporheic flowpaths, which we link to stream morphology and streamflow, on prevailing hyporheic redox conditions and on biogeochemical transformations occurring within streambeds. We focus on the dissolved inorganic reactive forms of nitrogen, ammonium and nitrate, because nitrogen is one of the most common reactive solutes and an essential nutrient found in stream waters. Our objectives are to explore the influence of stream morphology, hyporheic water temperature and relative abundance of ammonium and nitrate, on transformation of ammonium, removal of nitrates and production of nitrous oxide, a potent greenhouse gas. We address our objectives with analytical solutions of the Multispecies Reactive Advection-Dispersion Equation coupled with linearized Monod's kinetics and analytical solutions of the hyporheic flow for alternate-bar morphology. We introduce a new Damköhler number, Da, defined as the ratio between the median hyporheic residence time and the time scale of oxygen consumption, which we prove to be a good indicator of where aerobic or anaerobic conditions prevail. In addition, Da is a key index to quantify hyporheic nitrification and denitrification efficiencies and defines a new theoretical framework for scaling results at both the morphological-unit and stream-reach scales.