Electronic excitations near the surface of water ice lead to the desorption of adsorbed molecules, through a so far debated mechanism. A systematic study of photon-induced indirect desorption, revealed by the spectral dependence of the desorption (7 to 13 eV), is conducted for Ar, Kr, N2, and CO adsorbed on H2O or D2O amorphous ices. The mass and isotopic dependence and the increase of intrinsic desorption efficiency with photon energy all point to a mechanism of desorption induced by collisions between adsorbates and energetic H or D atoms, produced by photodissociation of water. This constitutes a direct and unambiguous experimental demonstration of the mechanism of indirect desorption of weakly adsorbed species on water ice, and sheds new light on the possibility of this mechanism in other systems. It also has implications for the description of photon-induced desorption in astrochemical models.