He “passed away peacefully at 12:25 this afternoon” at his home in Selsey, West Sussex, they said in a statement.
Sir Patrick presented the BBC programme The Sky At Night for over 50 years, making him the longest-running host of the same television show ever.
He wrote dozens of books on astronomy and his research was used by the US and the Russians in their space programmes.
Described by one of his close friends as “fearlessly eccentric”, Sir Patrick was notable for his habit of wearing a monocle on screen and his idiosyncratic style.
Sir Patrick presented the first edition of The Sky at Night on 24 April 1957. He last appeared in an episode broadcast on Monday.
A statement by his friends and staff said: “After a short spell in hospital last week, it was determined that no further treatment would benefit him, and it was his wish to spend his last days in his own home, Farthings, where he today passed on, in the company of close friends and carers and his cat Ptolemy.
The Sky at Night is the longest running television program in the world.