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.

Mr Grivas said the islands had been in his family for over 150 years but they could no longer afford to keep the properties.

Greek media have reported that the Sheikh wants an island for each of his 24 children.

Unfortunately, the Echinades are a chain of 18 islands, meaning the emir will have to find another six elsewhere.

The emir also appears to be set for a long battle with Greek officials over his plans for developing the islands.

Mr Kassianos said that, whatever the size of the land, the home can be no bigger than 250 square metres.

“The emir has reacted to this saying his WC is 250 square metres and his kitchen alone has to be 1,000 square metres, because otherwise how is he going to feed all his guests?” he said.

The deal was announced a month after the Greek premier, Antonis Samaras, flew to Doha to rebuild ties strained by continuous delays on the Greek side over Qatari investment in Greece.

The emir had pledged to invest up to 5billion euros in Greece’s transport and infrastructure when it was hit by the economic crisis three years ago.

He had been put off by Greece’s red tape and inefficiency but relations have improved, with Qatar now bidding to redevelop the Hellenikon airport site near Athens.

If the deal goes through, the airport could serve as an international hub for Qatar Airways.

Qatar may also bid for the Astir Palace hotel, a beachfront hotel near Athens that is popular with Arab tourists.

Despite Greece’s extensive privatisation programme, it has been suggested that Greece should be prepared to sell off even more of its assets to help reduce its debt obligations to other countries.

Josef Schlarmann, a member of Merkel’s Christian Democrats party, has warned Greece that, as with insolvent individuals, it should expect to sell everything it has to repay its creditors.

84% of the German public believe the EU should not help Greece recover from the economic crisis.

It has been suggested that this could be raised by the sale of state-owned Greek islands, of which there are around 6,000.