The actor, who played soap villain Den Watts, had been surrounded by friends and co-stars and earlier reports said he was being monitored by doctors in a United Kingdom hospital.
This week, the soap star was being monitored by doctors after returning to the United Kingdom from Bulgaria.
Grantham's management company, Advocate Agency, said he died Friday but did not disclose the cause.
He enjoyed two popular spells in the BBC soap, with more than 30 million viewers tuning in to watch a 1986 Christmas Day episode in which his character served divorce papers to his onscreen wife, Angie.
He wrote: "What a life Leslie Grantham led".
Anita Dobson, who played his screen wife Angie, said: "I loved working with Leslie and I will never forget our time together on EastEnders".
Grantham's management, Advocate Agency, says he died Friday, June 15, 2018 but did not disclose the cause of death.
Kathy Beale actress Gillian Taylforth said: "I'm deeply saddened to hear the very sad news".
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Grantham is survived by his ex-wife, Jane Laurie, and three sons.
"They will not be making any statements to the media".
Den returned in the early 2000s after being supposedly killed off in 1989, before leaving for good in 2005. They also ask that no photographs be taken of them in their grief.
According to The Sun, close friends and pals in the showbiz industry had been visiting him in hospital this week.
He is thought to have been in Bulgaria to star in a TV series called "The English Neighbour".
He was convicted for murdering a West German taxi driver while serving in the army in 1967, which saw him imprisoned for a "life sentence" of 10 years.