Her daughter, actress Rachael Stirling, said she died of cancer, after being diagnosed in March.
"She spent her last months joyfully reflecting on her extraordinary life, full of love, laughter and a deep pride in her profession," she added.
Dame Diana also played the only woman who became Mrs James Bond.
She played Tracy, who married George Lazenby's 007 in the 1969 film On Her Majesty's Secret Service.
Lazenby said he was "so sad" to hear of her death, while Bond producers Michael G Wilson and Barbara Broccoli also paid tribute.