Her daughter, actress Rachael Stirling, said she died of cancer, after being diagnosed in March.
Her agent Simon Beresford said she "died at home with her family who have asked for privacy at this hard time".
Rigg's agent said: "It is with tremendous sadness that we announce that Dame Diana Rigg died peacefully early this morning".
Rigg, survived by a daughter Rachael Stirling, is a highly celebrated of British artistic culture, winning accolades such as a Tony Award, BAFTA TV Award, and many more.
Even at the age of 75, Rigg proved that she still had some serious acting chops when she took the part of Olenna Tyrell (aka the Queen of Thorns) on HBO's Game of Thrones.
Rigg spent several years in the 1960s as a member of the Royal Shakespeare Company, and combined screen work with an acclaimed stage career, in plays including Bertolt Brecht's "Mother Courage" and Tom Stoppard's "Jumpers" at the National Theatre in London.
In 2017, she underwent heart surgery after falling ill.
In 2000, Dame Diana's achievements over her long career were recognised again by Bafta with the special award. All of these roles earned her a Tony nomination, and the latter resulted in a win.
He added that Rigg would be "greatly missed". But I do remember after the final curtain came down that I was having a glass of wine in the bar with the director and she came and put her hand on my shoulder and said: 'Now David, I really think you need a holiday.' She could be very warm.
Rigg amassed an extensive acting resume over her almost 60-year-long career.
'I'm so sad to hear of the death of Diana Rigg, ' he writes. She always raised the bar with her incredible talent, intelligence and wit.
She's now appearing in the new series of All Creatures Great and Small as Mrs Pumphrey.
She returned to the West End in 2011 to play Mrs Higgins in Pygmalion at the Garrick Theatre, having played Eliza 37 years previously. "Flinty, fearless, fabulous. There will never be another". She has also been credited with delivering one of the most memorable lines of the entire series when she told Nikolaj Coster-Waldau's Jaime Lannister, "Tell Cersei".