The giant radio galaxy M87 was observed at GeV/TeV gamma-ray energies with the H.E.S.S. (High Energy Stereoscopic System) Cherenkov telescopes in the years 2003-2006. The observations confirm M87 as the first extragalactic TeV gamma-ray source not of the blazar type (first indications of a signal were reported by the HEGRA collaboration earlier). The TeV gamma-ray flux from M87 as measured with H.E.S.S. was found to be variable on time-scales of years and surprisingly also of days which strongly constrains the size of the emission region. The results (position, energy spectrum and light curve) as well as theoretical interpretations will be presented.