The astronomer and broadcaster "passed away peacefully at 12.25pm this afternoon", according to a statement released by his friends and family.
Dr Brian May was at Moore's bedside and was with the Sky At Night presenter during his last hours.
The Queen guitarist and close friend of Moore tweeted: "Patrick was very peaceful in his last hours. With his beloved cat Ptolemy purring on his bed. And his pals all around. A great innings."
Sir Terry Pratchett, the Discworld author and friend, reminisced about his time with the broadcasting legend. "Our fondest memory will always remain eating astronomers chilli with Patrick Moore & @drbrianmay at 3am during a Perseid shower. A legend," he wrote.
[Close friends Dr Brian May and Sir Terry Pratchett]
Moore's contribution to the world of astronomy was extensive. He wrote many books on the subject, and his research was even used by the US and the Russians in their space programmes.
The astronomer also held the accolade of being the longest-running presenter of a TV programme, having fronted The Sky at Night since the first show in 1957.
Fellow television presenter and scientist Professor Brian Cox posted a message on Twitter, saying: "Very sad news about Sir Patrick. Helped inspire my love of astronomy. I will miss him!"
He continued: "Patrick certainly leaves a wonderful legacy, though. The generations of astronomers and scientists he introduced to the night sky."
Presenters Eamonn Holmes and Sue Perkins also paid their respects via Twitter.
[Holmes and Professor Cox]
Holmes wrote: "A man I've admired from childhood. Sir Patrick Moore has died - great character .... Finally he's going up amongst the Heavens. #RIP."
Echoing the broadcaster's well-known catchphrase, Perkins tweeted: "RIP Patrick Moore - you taught me to look up x"
Acting Director of BBC Television Roger Mosey also said: "Patrick Moore was one of the great educators of modern television. He inspired people to study astronomy. We and our audiences will miss him."