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, suppressing methane (CH4) production and increasing carbon dioxide (CO2) production. Current large-scale models of Arctic C cycling do not include Fe cycling or pH interactions. Here, we coupled Fe redox reactions and C cycling in a geochemical reaction model to simulate the interactions of SOM decomposition, Fe(III) reduction, pH dynamics, and greenhouse gas production in permafrost soils subject to dynamic hydrology. We evaluated 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 higher frequency oxic-anoxic cycles, rapid oxidation of Fe(II) to Fe(III) during oxic periods and gradual Fe(III) reduction during anoxic periods reduced cumulative CH4 fluxes and increased cumulative CO2 fluxes. Lower pH suppressed CH4 fluxes through its direct impact on methanogenesis and by increasing Fe(III) bioavailability. Our results suggest that models that do not include Fe-redox reactions and its pH dependence could overestimate CH4 production and underestimate CO2 emissions and SOM decomposition rates in Fe-rich, frequently waterlogged Arctic soils.