  Many galaxy clusters have giant halos of non-thermal radio emission,
indicating the presence of relativistic electrons in the clusters. Relativistic
protons may also be accelerated by merger and/or accretion shocks in galaxy
clusters. These cosmic-ray (CR) electrons and/or protons are expected to
produce gamma-rays through inverse-Compton scatterings or inelastic $pp$
collisions respectively. Despite of intense efforts in searching for
high-energy gamma-ray emission from galaxy clusters, conclusive evidence is
still missing so far. Here we report the discovery of $\ge 200$ MeV gamma-ray
emission from the Coma cluster direction with an unbinned likelihood analysis
of the 9 years of {\it Fermi}-LAT Pass 8 data. The gamma-ray emission shows a
spatial morphology roughly coincident with the giant radio halo, with an
apparent excess at the southwest of the cluster. Using the test statistic
analysis, we further find tentative evidence that the gamma-ray emission at the
Coma center is spatially extended. The extended component has an integral
energy flux of $\sim 2\times 10^{-12}{\rm \ erg\ cm^{-2}\ s^{-1}}$ in the
energy range of 0.2 - 300 GeV and the spectrum is soft with a photon index of
$\simeq-2.7$. Interpreting the gamma-ray emission as arising from CR proton
interaction, we find that the volume-averaged value of the CR to thermal
pressure ratio in the Coma cluster is about $\sim 2\%$. Our results show that
galaxy clusters are likely a new type of GeV gamma-ray sources, and they are
probably also giant reservoirs of CR protons.
