Wetlands and flooded peatlands can sequester large amounts of carbon (C) and have high greenhouse gas mitigation potential. There is growing interest in financing wetland restoration using C markets; however, this requires careful accounting of both CO2 and CH4 exchange at the ecosystem scale. Here we present a new model, the PEPRMT model (Peatland Ecosystem Photosynthesis Respiration and Methane Transport), which consists of a hierarchy of biogeochemical models designed to estimate CO2 and CH4 exchange in restored managed wetlands. Empirical models using temperature and/or photosynthesis to predict respiration and CH4 production were contrasted with a more process‐based model that simulated substrate‐limited respiration and CH4 production using multiple carbon pools. Models were parameterized by using a model‐data fusion approach with multiple years of eddy covariance data collected in a recently restored wetland and a mature restored wetland. A third recently restored wetland site was used for model validation. During model validation, the process‐based model explained 70% of the variance in net ecosystem exchange of CO2 (NEE) and 50% of the variance in CH4 exchange. Not accounting for high respiration following restoration led to empirical models overestimating annual NEE by 33–51%. By employing a model‐data fusion approach we provide rigorous estimates of uncertainty in model predictions, accounting for uncertainty in data, model parameters, and model structure. The PEPRMT model is a valuable tool for understanding carbon cycling in restored wetlands and for application in carbon market‐funded wetland restoration, thereby advancing opportunity to counteract the vast degradation of wetlands and flooded peatlands. Key Points Using model‐data fusion, we parameterized a hierarchy of biogeochemical models used to estimate CO2 and CH4 exchange in restored wetlands In a validation exercise, the PEPRMT model was able to explain 70% and 50% of the variance in net exchange of CO2 and CH4, respectively Simulation of soil carbon availability was critical for accurately predicting CO2 exchange in recently restored wetlands