The announcement was made late on Tuesday afternoon by the island's police chief, who said that an investigation is underway to determine the cause of death and that all possibilities are being examined.
The 60-year-old was on the island to participate in a scientific conference at the Orthodox Academy and had been missing since July 2, when a search was launched to find her. Her remains were found by a local residents about 10 kilometres from the area where authorities had focused their search.
The body was found in the middle of the cave and the face was not visible, though it was clothed in the same clothing as that worn by Eaton at the time of her disappearance. Police had not officially confirmed the identity of the body, however, until the relevant procedures were completed.
A forensic investigation is being carried out to determine whether the woman's death was the result of foul play. The body was recovered by an EMAK emergency rescue team and taken to Rethymno hospital for an autopsy.