Leslie was best-known for playing "Dirty" Den Watts in "EastEnders", winning over legions of fans with his two stints as the villainous character.
It is understood before his death Mr Grantham had recently moved back to the United Kingdom, after living in Bulgaria.
'His ex-wife and sons have asked for their privacy to be respected at this hard time'.
"They will not be making any statements to the media".
Gillian Taylforth, who plays Kathy Beale, also spoke of her "many happy memories" of working with Leslie and added: "Those iconic Christmas episodes were legendary and they will always be part of EastEnders history".
"We extend our deepest sympathies and condolences to his family and friends at this extremely hard time".
EastEnders's executive consultant John Yorke paid tribute on behalf of the BBC soap, saying: "Everyone at EastEnders is deeply saddened to hear that Leslie has passed away".
A representative for Grantham confirmed his passing on Friday morning.
According to The Sun, the screen star had been visited in hospital by close friends in the industry.
Leslie moved out of the United Kingdom in 2015 after splitting from his wife Jane Laurie after 31 years of marriage, setting up home in Bulgaria.
Grantham's life was not without controversy.
He even took his talents overseas, finding fame on Bulgarian TV series The English Neighbour.
The character was apparently murdered in 1989, but made a shock return to Albert Square in 2003.
He and Anita [Dobson, who played Sharon's mum Angie] looked after me in my early days and showed me the ropes, always with care and kindness.
Broadcaster Paul Ross remembered him as a "talented, kind and very amusing man", while Craig Fairbrass - who played Dan Sullivan in EastEnders - said he had been "a strong role model".