His son, Adam said he died of end-stage chronic obstructive pulmonary disease on Friday morning.
Nimoy had a long career as both an actor and director.
However, Nimoy was best known for his portrayal of the half-human, half-Vulcan character in both the TV franchise and series of films.
Known for suppressing his emotions and using strict logic to guide his actions, Spock became one of the best-known and most beloved sci-fi characters of the late 20th century.
Last year, the US actor revealed he was suffering from chronic lung disease, despite stopping smoking more than 20 years ago.
It was reported earlier this week that Nimoy had been taken to hospital on 19 February after suffering from chest pains.
He later tweeted: “A life is like a garden. Perfect moments can be had, but not preserved, except in memory.”
Nimoy also signed off with “LLAP” – a reference to his character’s famous catchphrase, “Live long and prosper,” which was to be his final tweet.
George Takei, a friend of Nimoy who featured as Hiraku Sulu on Star Trek, also paid tribute to the deceased actor.
“The word extraordinary is often overused but I think it’s really appropriate for Leonard, he was extraordinarily talented man, also a very decent human being,” Mr Takei said.