For temperature and humidity control of proton exchange membrane fuel cell (PEMFC) reactants, a membrane based external humidification system was designed and constructed. Here we develop and validate a physics based, low-order, control-oriented model of the external humidification system dynamics based on first principles. This model structure enables the application of feedback control for thermal and humidity management of the fuel cell reactants. The humidification strategy posed here deviates from standard internal humidifiers that are relatively compact and cheap but prohibit active humidity regulation and couple reactant humidity requirements to the PEMFC cooling demands. Additionally, in developing our model, we reduced the number of sensors required for feedback control by employing a dynamic physics based estimation of the air-vapor mixture relative humidity leaving the humidification system (supplied to the PEMFC) using temperature and pressure measurements. A simple and reproducible methodology is then employed for parameterizing the humidification system model using experimental data.