A combined experimental and first principles study of Cu defects in bulk ZnO is presented. Cu particles are epitaxially deposited on the polar O-ZnO(000 (1) over bar) surface at room temperature. Upon heating, a broadening of the quasielastic peak in high resolution electron energy loss spectra is observed, corresponding to an electronic doping effect of Cu atoms in bulk ZnO with an ionization energy of 88 meV. Cu impurities in ZnO, although commonly acting as acceptors, are presently observed to induce shallow donor states. We assign these to interstitial Cu species on the basis of a hybrid density functional study.