Publicist Rick Miramontez said Redgrave passed peacefully Sunday night at her beloved home in Connecticut surrounded by her children, Ben, Pema and Annabel, as well as close friends.
In a statement released through Miramontez, the children announced, "Our beloved mother Lynn Rachel passed away peacefully after a seven year journey with breast cancer," Redgrave's children said in their May 3 statement. "She lived, loved and worked harder than ever before. The endless memories she created as a mother, grandmother, writer, actor and friend will sustain us for the rest of our lives. Our entire family asks for privacy through this difficult time."
A master of stage and screen, Redgrave helped carry the torch of an acclaimed acting family including father Michael Redgrave, sister Vanessa Redgrave, brother Corin Redgrave, nieces Natasha Richardson and Joely Richardson and screenwriter-director nephew Carlo Nero.
Redgrave's death is another blow to this close-knit tribe, following the deaths of Natasha Richardson last year and Corin Redgrave a mere month ago.
The actress received Oscar nominations for her roles in Georgy Girl and Gods and Monsters, and Tony nominations for her roles in Mrs Warren's Profession, Shakespeare for My Father and The Constant Wife.
"All the films I've been in -- and I haven't been in that many attention-getting films -- no one expected anything of, least of all me," she told the AP in 1999. "Vanessa was the one expected to be the great actress. It was always: Corin's the brain, Vanessa the shining star, oh, and then there's Lynn."
Diagnosed with breast cancer in December 2002, Redgrave had a mastectomy in January 2003 and began chemotherapy treatments.
She is survived by three children, six grandchildren, sister Vanessa and four nieces and nephews.
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