Non-perturbative quantum-gravity effects can change the fate of black holes and make them bounce in a time scale shorter than the Hawking evaporation time. In this article, we show that this hypothesis can account for the GeV excess observed from the galactic center by the Fermi satellite. By carefully taking into account the secondary component due to the decay of unstable hadrons, we show that the model is fully self-consistent. This phenomenon presents a specific redshift-dependance that could allow to distinguish it from other astrophysical phenomena possibly contributing to the GeV excess.