By Agence France-Presse
"His Royal Highness Prince Henrik died Tuesday, February 13 at 23:18 at Fredensborg Castle", a royal residence about 40 kilometres (25 miles) north of Copenhagen, surrounded by his wife and their two sons, the palace statement said.
The palace had warned Tuesday that the prince, who had been in hospital since January 28 for a lung infection, had returned home "to spend his last days".
Born Henri Marie Jean Andre de Laborde de Monpezat on June 11, 1934 in Talence, near Bordeaux, the count married Margrethe, heir to the Danish throne, in June 1967.
Margrethe was crowned in January 1972 and Henrik made no secret of his disappointment that his royal title was never changed to king, which did little to endear him to the Danish people.
He was diagnosed with dementia in September 2017.
The prince retired from public service in 2016, and the following year he revealed that he did not want to be buried next to his wife because he was never made her equal.
Royal couples are traditionally buried together in Roskilde Cathedral, west of Copenhagen.
The palace statement did not say where the prince would be buried.