  Observations of the Galactic center region with the H.E.S.S. telescopes have
established the existence of a steady, extended source of gamma-ray emission
coinciding with the position of the super massive black hole Sgr A*. This is a
remarkable finding given the expected presence of dense self-annihilating Dark
Matter in the Galactic center region. The self-annihilation process is giving
rise to gamma-ray production through hadronization including the production of
neutral pions which decay into gamma-rays but also through (loop-suppressed)
annihilation into final states of almost mono-energetic photons. We study the
observed gamma-ray signal (spectrum and shape) from the Galactic center in the
context of Dark Matter annihilation and indicate the prospects for further
indirect Dark matter searches with H.E.S.S.
