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Natalie Christopher, who comes from London but lived in Cyprus and was on holiday in Greece, had been reported missing by her partner after going for a run on Monday morning.
Authorities launched a search operation involving police, the fire brigade and a helicopter.
"The body of the 35-year-old British national was found by search teams at a ravine about 20 metres deep," Greek police said, confirming earlier reports by state TV ERT.
It did not provide further details.
Christopher was a sports enthusiast who also ran summer camps to get girls more involved in sports. Her Facebook page suggested her hobbies also included rock climbing.
A person who participated in the rescue operation, Vaggelis Kriaras, told Greece's Open TV that Christopher may have fallen in her attempt to climb, or descend, a cliff-face.
"Unfortunately it appears she caught onto a rock which came away and crushed her," he said, citing accounts from others in the rescue operation.
Christopher's disappearance had prompted a massive campaign on social media with friends pleading for information on her whereabouts. Cyprus's Justice Minister George Savvides said he was "profoundly shocked" by Christopher's death and offered condolences to her family and friends.
Christopher was well-known for her peace activism in ethnically-split Cyprus and was also a campaigner for more women in under-represented scientific fields.
Unite Cyprus Now, a grassroots group of which Christopher was a member, said : "You touched our lives with energy and dedication to make this world a better place."