Rees, who starred in BBC drama series Poldark in the 1970s, was 63.
In a statement, her family said they were "deeply saddened" and the actress, who also enjoyed an extensive theatre career, would 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 said.
Rees was married to the late Dynasty actor Christopher Cazenove for more than 20 years and they had two sons together, Linford and Rhys, 35.
Linford, the elder of the two, died in a car crash on the M11 in Essex in 1999 aged 25.
In 1994 the actress divorced Cazenove and went on to marry David McAlpine, of the construction family, in 2005, with whom she lived in London.
Rees played Demelza in Poldark, a costume drama based on the novels written by Winston Graham and first broadcast in the UK between 1975 and 1977.
She also had a role in cult classic Jack the Ripper film Hands Of The Ripper and on stage she appeared in A Winter's Tale, Richard II and Romeo And Juliet.
In addition to her acting success, she also founded an eponymously titled jewellery design company based in Knightsbridge, with her pieces featured in the film Elizabeth, The Golden Age.
Her family said she remained an active supporter of the arts and was an honorary fellow of the Royal Welsh College of Music and Drama in Cardiff, the city where she grew up as a young child.
Her funeral will be private but there are plans for a service in celebration of her life which will be announced at a later date.

Martin, 28, has scored seven goals in 17 appearances for Fulham in the Championship this term.
He "made himself unavailable" for Friday's abandoned game at Reading, but Jokanovic insisted he would stay.
"I'm not going to send him back to Derby - he's going to stay with us and respect the contract," said Jokanovic.
"He stopped in training, but I have information from the medical staff that he is available to play. He decided to take a day off."
He continued to BBC Radio London: "We're not a train station, you can't come in and out when you want. We need to respect ourselves, we are the oldest London club.
"I don't know if he will play for Fulham, but I'm sure he's not going to play for Derby."
Earlier this month, Derby manager Steve McClaren said he was surprised Martin was allowed to leave the club under previous boss Nigel Pearson.
Welsh actress Angharad Rees has died after a long battle with cancer, her family has said.
[NEXT_CONCEPT]
Fulham manager Slavisa Jokanovic has dismissed reports that striker Chris Martin could return early to Derby from his season-long loan at Craven Cottage.