The palace made the announcement via a press statement on Tuesday, adding that Prince Henrik's condition "remains serious".
"His Royal Highness Prince Henrik was today transferred from the hospital to Fredensborg Palace, where the prince wishes to spend his last days," the palace said.
Royal Family press spokesperson Lene Balleby confirmed to the Billed-Bladet magazine that the prince had asked to be moved to Fredensborg.
"There, the prince can be surrounded by family and be in a place that means something to him," Balleby said.
Denmark's Crown Prince couple, Frederik and Mary, arrived at Fredensborg just after 3pm on Wednesday, around two hours after Prince Henrik.
Fredensborg Palace on February 13th, 2018. Photo: Mads Claus Rasmussen/Scanpix Denmark
Prince Henrik was admitted to Copenhagen's Rigshospitalet on January 28th for a tumour in his left lung which turned out to be benign, and a pulmonary infection. In September 2017, he was diagnosed with dementia.
Crown Prince Frederik, 49, cut short his visit to the Winter Olympics in Pyeongchang to return home to his sick father last week.
Henrik retired from public service in January 2016. Last year, he announced that he did not want to be buried next to his wife, thereby breaking with the tradition of burying royal spouses together in Roskilde Cathedral, west of Copenhagen.
Born Henri Marie Jean Andre de Laborde de Monpezat on June 11th, 1934 near Bordeaux, he married Margrethe, then crown princess, in 1967.
Henrik and Margrethe have another son, Prince Joachim, who is 48, and eight grandchildren.