She was 86.
In a statement, her three children said their "adored mother" died on Wednesday.
"We will always remember her endless capacity for joy, her ability to comfort every heartache, her beautiful way with words and her expert guidance in all things," her children Miriam, Rebecca and Joshua Wilcox said.
Over the decades, Rantzen became one of the most respected figures within British media, helping her to establish charities that helped both the young and old.
She was perhaps most famous for fronting the BBC consumer affairs program That's Life! for 21 years from 1973 to 1994.
Over the years, the show branched out beyond consumer affairs to investigate life-and-death issues, including an investigation into how a boarding school employed pedophiles and a critique of the UK's lack of organ donors. It could also be light-hearted, blending satire and farce with the more hard-hitting segments.
The program led her to set up Childline in 1986, a helpline for children in danger or distress that was open 24/7 throughout the year. She later launched The Silver Line in 2012, which aimed to tackle loneliness in older people.
"Her legacy of compassion and understanding will live on in her charities Childline and The Silver Line, and through those of us who were lucky enough to love and be loved by her," her children said.
Rantzen was appointed a dame in 2015 by Queen Elizabeth II for services to children and older people through Childline and The Silver Line.
In later life, Rantzen became a strong proponent for assisted dying, after she was diagnosed with stage four lung cancer in 2023. She openly discussed her own plan to "buzz off to Zurich" because assisted dying is legal in Switzerland, and she criticised the "messy and cruel" law in England and Wales that would criminalise loved ones who tried to help in any endeavour to do so.
Earlier in September, ahead of a vote in parliament where the latest effort to legalise assisted dying was defeated, Rantzen said it was too late for her to travel, because she had become "too physically fragile to make the journey."
Tributes poured in for Rantzen, with particular praise for her campaigning and charitable work.
"Through her decades of campaigning, including founding Childline and The Silver Line, she changed countless lives and gave a voice to people who often went unheard," British Prime Minister Andy Burnham said.
"And I will always admire the characteristic courage and openness with which she spoke about her illness, making us all think about the difficult questions we face at the end of life."
Rantzen was married to Desmond Wilcox, a television producer and documentary maker, who died in 2000.
"We are grateful she is finally at rest with her beloved husband, Desmond Wilcox, but we will miss her immeasurably," her children said.
"She was our sunshine."
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