The islands are part of a small archipelago known as the Echinades, a couple of miles from Ithaca, a famous site in Homer’s Odyssey.
They first caught the eye of the emir, 56-year-old Sheikh Hamad bin Khalifa al-Thani, when he moored his super-yacht nearby whilst on holiday four years ago.
The £4.2million deal for Oxia, the largest of the islands at 1,200 acres, was agreed last year but had been held up by delays in obtaining land use permits from Greek forestry officials, according to the Financial Times.
Ithaca’s Greek-American mayor, Ioannis Kassianos, said: “When you buy an island, even if you are the emir of Qatar, it takes a year and a half for all the paperwork to go through.”
The emir also agreed a £3m deal last week for a further five islands nearby with David Grivas, whose family has owned them since the inception of modern Greece, the Guardian reported.