Staff at the private Hygeia Hospital in Athens confirmed to The Associated Press that Constantine had died after treatment in an intensive care unit but had no further details pending an official announcement.
The former Greek king was married to Queen Anne-Marie, Queen Margrethe's sister.
He was admitted to a hospital in Athens on Saturday and was in critical condition after suffering a stroke.
Several Greek media reported that Constantine had suffered a stroke at his home.
Constantine has been hospitalized several times in recent years. He has been affected by covid-19 twice.
Constantine was the king of Greece from 1964 until 1967 when Greek army officers seized power in a coup.
He attempted a counter-coup, which failed, and he and the then Queen Anne-Marie were forced into exile.
To his final days, while accepting that Greece was now a republic, Constantine continued to style himself King of Greece and his children as princes and princesses even though Greece no longer recognized titles of nobility.
For most of his years in exile, he lived in Hampstead Garden Suburb, London, and was said to be especially close to his second cousin Charles, the Prince of Wales and now King Charles III.
While it took Constantine 14 years to return to his country, briefly, to bury his mother, Queen Federica in 1981, he multiplied his visits thereafter and, from 2010, made his home there. There were continued disputes: in 1994, the then-socialist government stripped him of his nationality and expropriated what remained of the royal family’s property. Constantine sued at the European Court of Human Rights and was awarded 12 million euros in 2002, a fraction of the 500 million he had sought.
Constantine travelled with a Danish passport as a Danish prince.
He is survived by his wife, the former Princess Anne-Marie of Denmark; youngest sister of Queen Margrethe II; five children, Alexia, Pavlos, Nikolaos, Theodora and Philippos; and nine grandchildren.
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