A statement from his agent said he died on Friday morning and that a private funeral would be held.
Meanwhile, John Yorke, EastEnders' Executive Consultant, said in a statement: "Everyone at EastEnders is deeply saddened to hear that Leslie has passed away. RIP big man... loved working with ya in panto... you made me laugh and I learnt a lot from you too. absolutely gutted".
Brown said Grantham was "a wonderful and special actor, witty and very talented", and that she will "remember him very fondly and with affection".
Grantham shot to fame when he was cast as the landlord of the Queen Vic, the east London public house around which the action in EastEnders revolves.
His tumultuous marriage to alcoholic wife Angie captivated the nation and more than 30 million people - at the time over half of the United Kingdom population - tuned in to the 1986 Christmas special to watch Den present her with divorce papers. "My heart goes out to his loved ones".
Grantham's final appearance in EastEnders was on the soap's 20th anniversary.
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And if that's the way people took it, I apologize to them, but that's not the way it was taken. He carded a 10 on the hole for a 5 over par.
Richie added that Grantham was "a natural charmer & genuinely gracious, he had his demons but don't we all!"
"Everyone thought Den was a lovable rogue", Grantham said later.
The tribute read: "In memory of Leslie Grantham 1947-2018".
The announcement follows news earlier this week that Grantham had returned to the United Kingdom from Bulgaria to receive medical attention.
According to The Sun, close friends and pals in the showbiz industry had been visiting him in hospital this week. Grantham was divorced from his wife of 31 years Jane Laurie in 2013, and is survived by his three grown-up children. In 2010, he spent time in Bulgaria filming TV series The English Neighbour.
He took up a career in acting after being released from prison, following a ten year stint for the death of a West German taxi driver in 1966.