The Danish royal palace shared the news in an official statement, revealing that Joachim left the University Hospital of Toulouse in France on Monday evening.
The statement added: "It is now the opinion of the doctors that the prince's health has improved to such an extent that His Royal Highness can be discharged, and Prince Joachim is now staying at the Château de Cayx. It is still the family's wish that the prince has the necessary peace to recover completely."
WATCH: A look at some of the most beautiful royal residences
It concluded: "Prince Joachim and Princess Marie would like to take this opportunity to thank the hospital staff involved for a professional course."
The royal underwent successful surgery on 25 July, after which he was taken to intensive care. After the operation, the palace gave an update, saying: "The blood clot in the brain was due to a sudden dissection of an artery, and the hospital's medical team estimates that the risk of recurrence is very small once the artery has healed.
"Prince Joachim is expected to be moved from the intensive care unit soon, but will continue to be hospitalised in the near future."
Joachim with his four children, wife Marie and ex-wife Alexandra
Joachim had been spending his summer break at the Danish royal family's French residence Château de Cayx, located in the middle of the Cahors vineyard.
The castle dates back to the early 15th century, and was bought by Queen Margrethe and Prince Henrik of Denmark in 1974. Over the years, the Queen and Prince restored and transformed the property, as well as re-establishing a prestigious winery stretching across close to 24 hectares of land.
Joachim is holidaying with his Parisian wife Princess Marie and their two children Princess Athena and Prince Henrik. They were also joined for a period by Joachim's ex-wife Countess Alexandra of Frederiksborg and the former couple's two sons Prince Nikolai and Prince Felix, to celebrate the latter's 18th birthday in July.
Make sure you never miss a ROYAL story! Sign up to our newsletter to get all of our celebrity, royal and lifestyle news delivered directly to your inbox.