  Using gamma-ray data from the Fermi Large Area Telescope, various groups have
identified a clear excess emission in the Inner Galaxy, at energies around a
few GeV. This excess resembles remarkably well a signal from dark-matter
annihilation. One of the most compelling astrophysical interpretations is that
the excess is caused by the combined effect of a previously undetected
population of dim gamma-ray sources. Because of their spectral similarity, the
best candidates are millisecond pulsars. Here, we search for this hypothetical
source population, using a novel approach based on wavelet decomposition of the
gamma-ray sky and the statistics of Gaussian random fields. Using almost seven
years of Fermi-LAT data, we detect a clustering of photons as predicted for the
hypothetical population of millisecond pulsar, with a statistical significance
of 10.0 sigma. For plausible values of the luminosity function, this population
explains 100% of the observed excess emission. We argue that other
extragalactic or Galactic sources, a mismodeling of Galactic diffuse emission,
or the thick-disk population of pulsars are unlikely to account for this
observation.
