The pursuit of a material capable of storing a high capacity of hydrogen (H-2) efficiently has prompted us to study the structural, electronic and H-2 storage properties of recently designed two-dimensional BN2 nanosheets. Our spin-polarized density functional theory based calculations have revealed that the pristine BN2 barely anchor H-2 molecules, however, alkali metal (AM) doping enhances the binding energies drastically. Van der Waals corrected energetics analysis established a uniform distribution of AMs over the BN2 monolayers even at a high doping concentration of 12.50%, which ensure the reversibility of the systems. Bader charge analysis, Roby-Gould bond index method, and electron localization function isosurfaces conclude the transfer of charges from AMs to BN2, which has resulted into strong ionic bonds between the former and the latter. The presence of partial positive charges on each of the AMs would adsorb multiple H-2 molecules with binding energies that are ideal for mobile H-2 storage applications. Considerably high H-2 storage capacities of 6.75%, 6.87% and 6.55% could be achieved with 3Li@BN2, 3Na@BN2 and 3K@BN2 systems, respectively that guarantees the promise of AMs decorated BN2 as a promising H-2 storage material.