"My dear old man, my beautiful dad, the most gentle of men, has passed away.
"I'm posting this because I know there are people all over the world who's (sic) heart he touched and who's ribs he tickled with his sparkly eyes and his cheeky attitude to everyone, and everything, and this is probably as efficient a method as any to pass on the news."
John was born in Christchurch and died in Coffs Harbour, NSW, which he has called home for the past 25 years.
Last April Crowe shared a photo of his father to Instagram alongside the caption: "Isolating with the old man. 84 now."
"Wearing a hat I got at Princeton while shooting A Beautiful Mind."
John's brother is New Zealand cricket star Dave Crowe, and Martin and Jeff Crowe are his nephews.