In an effort to design new functionalized nanostructures for clean energy storage, DFT calculations of Fen (n = 1-3) clusters on BC3 and BN monolayers are performed. The stability of the systems was considered by calculating the binding energies of the monolayers with Fen clusters on one or both sides. All the clusters bound strongly to both the monolayers and transferred electron density to the sheets. The cationic Fe clusters were then able to adsorb multiple H2 molecules through electrostatic and van der Waals interactions. The average adsorption energies per H2 in the case of maximum coverage were calculated to be -0.389 and -0.358 eV for systems with one Fe on both sides of BC3 and BN monolayers, respectively. In these cases four H2 molecules were adsorbed to the Fe atoms on both sides of the monolayer. These adsorption energies are such that there is potential for adsorption/desorption at ambient conditions. The results provide insights into an efficient and reversible storage of H2 by using Fen-functionalized BC3 and BN monolayers.