The electronic structure of ultrasmall Au clusters on thin MgO/Ag(001) films has been analyzed by scanning tunneling spectroscopy and density functional theory. The clusters exhibit two-dimensional quantum well states, whose shapes resemble the eigenstates of a 2D electron gas confined in a parabolic potential. From the symmetry of the highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO) of a particular cluster, its electron filling and charge state is determined. In accordance with a Bader charge analysis, aggregates containing up to 20 atoms accumulate one to four extra electrons due to a charge transfer from the MgO/Ag interface. The HOMO-LUMO gap is found to close for clusters containing between 70 and 100 atoms.