Ammonia and carbon dioxide play an important role in both atmospheric and interstellar ice chemistries. This work presents a theoretical and experimental study of the kinetics of the low-temperature NH3 and CO2 solid-state reaction in ice films, the product of which is ammonium carbamate (NH4+NH2COO-). It is a first-order reaction with respect to CO2, with a temperature-dependent rate constant fitted to the Arrhenius law in the temperature range 70 K to 90 K, with an activation energy of 5.1 ± 1.6 kJ mol-1 and a pre-exponential factor of 0.09-0.08+1.1 s-1. This work helps to determine the rate of removal of CO2 and NH3, via their conversion into ammonium carbamate, from atmospheric and interstellar ices. We also measure first-order desorption energies of 69.0 ± 0.2 kJ mol-1 and 76.1 ± 0.1 kJ mol-1, assuming a pre-exponential factor of 1013 s-1, for ammonium carbamate and carbamic acid, respectively.