The fate of organic carbon (C) in permafrost soils is important to the climate system due to the large global stocks of permafrost C. Thawing permafrost can be subject to dynamic hydrology, making redox processes an important factor controlling soil organic matter (SOM) decomposition rates and greenhouse gas production. In iron (Fe)-rich permafrost soils, Fe(III) can serve as a terminal electron acceptor, promoting anaerobic respiration of SOM and increasing pH. Current large-scale models of Arctic C cycling do not include Fe cycling or pH interactions. Here, a geochemical reaction model was developed by coupling Fe redox reactions and C cycling to simulate SOM decomposition, Fe(III) reduction, pH dynamics, and greenhouse gas production in permafrost soils subject to dynamic hydrology. We parameterized the model using measured CO2 and CH4 fluxes as well as changes in pH, Fe(II), and dissolved organic C concentrations from oxic and anoxic incubations of permafrost soils from polygonal permafrost sites in northern Alaska, United States. In simulations of repeated oxic-anoxic cycles, Fe(III) reduction during anoxic periods enhanced CO2 production, while the net effect of Fe(III) reduction on cumulative CH4 fluxes depended on substrate C availability. With lower substrate availability, Fe(III) reduction decreased total CH4 production by further limiting available substrate. With higher substrate availability, Fe(III) reduction enhanced CH4 production by increasing pH. Our results suggest that interactions among Fe-redox reactions, pH and methanogenesis are important factors in predicting CH4 and CO2 production as well as SOM decomposition rates in Fe-rich, frequently waterlogged Arctic soils.