A 27-year-old man detained in connection with her death had confessed to the crime, said Constantinos Lagoudakis, director general of the island's police directorate.
(L-R) Police Press Information Officer for Crete, Eleni Papathanasiou, Director of Security for Chania Police, Paris Chinopoulos, Chania Police Chief Giorgos Libinakis and Crete's Chief of Police Konstantinos Lagoudakis are seen during a news conference, presenting the latest developments on the murder.
He was due to be arraigned before a prosecutor on Tuesday, Lagoudakis said in a televised statement. In accordance with Greek law the suspect, a father of two, was not identified by name.
Eaton, who according to friends and relatives was trained in martial arts, was on Crete for a science conference.
She was thought to have been out jogging on the day she disappeared and colleagues raised the alarm when she failed to return. It is believed she died on the day of her disappearance, July 2, and a post mortem concluded asphyxiation was the cause.
Her body was found by cavers in the bunker, a system of man-made caves used by the Nazis during the occupation of Crete in World War Two.
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