The Welsh actress, best known for starring in BBC drama Poldark as Demelza in the 1970s, had been fighting a long battle with pancreatic cancer.
Rees's relatives said they were "deeply saddened" by her death, adding that she will be "greatly missed".
"Angharad passed away peacefully today with her family at her bedside in London, after a long battle with pancreatic cancer," her family told BBC News.
She is survived by her second husband David McAlpine - whom she married in 2005 - as well as youngest son Rhys, who is 35.
Her eldest son Linford died in a car crash in 1999, aged 25.
Rees was first married to fellow actor Christopher Cazenove, best known for his role in Dynasty, who died of septicaemia in April 2010.
Her funeral will be private but there are plans for a public service in celebration of her life, to be announced at a later date.