The actor was best known for portraying "Dirty" Den Watts in EastEnders from 1985 to 1989, before making a shock return to the BBC soap in 2003.
Grantham's management company, Advocate Agency, said he died Friday but did not disclose the cause.
A statement from his representative was released this morning, saying: "We formally announce the loss of Leslie Grantham, who passed away at 10.20am on the morning of Friday 15th June 2018".
'His ex-wife and sons have asked for their privacy to be respected at this hard time'.
A private funeral will be held for friends and family in due course.
EastEnders' classic Christmas Day 1986 episode, which saw Den give wife Angie (Anita Dobson) divorce papers, was watched by over 30m people in the UK.
Yet the star's lasting legacy is undoubtedly from his scene-stealing presence on EastEnders, where he constantly made waves on Albert Square with his villainous antics.
He left the United Kingdom after splitting with his wife of 31 years, Jane.
According to The Sun, close friends and pals in the showbiz industry had been visiting him in hospital this week.
Tracy, who starred as "Dirty" Den Watts' second wife Chrissie, wrote: "Really sorry to hear about Leslie Grantham".
He was reported to have been living in Bulgaria before his death, having gone there to appear in a TV series called The English Neighbour.
Presenter Paul Ross said: "Very sad to learn that Leslie Grantham has died".
Dobson, who played Grantham's on-screen wife Angie Watts in the soap, told BBC News: "He was a good-looking guy, he was a charmer, he was amusing, he was a good actor. You was West Ham, I am Spurs - but that didn't matter".
Prior to his EastEnders career, in 1967 he was convicted of murdering a German taxi driver while serving as a soldier, which he has always denied, and he went to prison until 1977.