Anne died this afternoon at a hospital in Morges, Switzerland, surrounded by family including four of her daughters, a statement said.
Michael, 94, who is suffering from cancer, visited her every day, the statement said.
Born Princess Anne of Bourbon-Parma, she met Michael in November 1947 at the wedding of the future Queen Elizabeth II and Philip Mountbatten in London.
Michael was forced to abdicate by the communists a month later and moved into exile.
"Michael lost a country but won an exceptional woman," commentator Stelian Tanase, an acquaintance of the royal couple, told The Associated Press. President Klaus Iohannis called her one of the "most important symbols of wisdom, dignity and a beacon of moral conduit."
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Her body will be flown from Switzerland to Romania on Thursday and will lie in state for one day in Peles Castle in the mountain resort of Sinaia where Michael was born, and then in the Royal Palace in Bucharest for one day.
Anne, who was half French and half Danish, married Michael in an Orthodox ceremony in Athens in 1948 after Pope Pius XII refused to give her dispensation to marry a non-Catholic. In 1966, the couple had another ceremony in a Catholic church in Monaco.
Anne is survived by Michael and their five daughters.