In the Mediterranean Sea, the probability that a large earthquake-triggered tsunami will occur in the coming decades is high. Historical tsunami database informs us on their geographical occurrence but their sources, i.e., the faults that slipped during earthquakes and displaced the seafloor to generate tsunamis, are often unknown. Here we identify the submarine rupture of the Amorgos earthquake that on July 9, 1956, triggered the largest mediterranean tsunami in the past two centuries. Using submarines, we explored major normal faults in the epicentral area, and discovered a large surface rupture along the 75-km long Amorgos fault. The 9.8-16.8-m large seafloor offset is compatible with a Mw7.5 event. This finding prompts a reassessment of the largest (≥20 m) tsunami wave origin, previously attributed to earthquake-triggered submarine mass-wasting. It demonstrates that tsunami source can be determined several decades after an event, a key information to better assess future seismic and tsunami hazards.