"It is with tremendous sadness that we announce the death of our beautiful, dynamic and one-of-a-kind mother," the statement said.
The British-born writer, sister of actress Joan Collins, died in Los Angeles, her spokeswoman said.
Collins's raunchy novels of the rich and famous sold more than 500 million copies in 40 countries.
In a career spanning four decades, all 32 of her novels appeared in the New York Times bestseller list.
The family statement said the writer lived "a wonderfully full life", adored by family, friends and readers.
"She was a true inspiration, a trailblazer for women in fiction and a creative force. She will live on through her characters but we already miss her beyond words," it added.
Collins was diagnosed with stage-four breast cancer six-and-a-half years ago, according to US celebrity magazine People.
She told the magazine in her last interview on 14 September that she had told few people about her diagnosis other than her three daughters, and did not regret her decision.
"I did it my way, as Frank Sinatra would say," she said.
"I've written five books since the diagnosis, I've lived my life, I've travelled all over the world, I have not turned down book tours and no-one has ever known until now when I feel as though I should come out with it."
She was in the UK less than a fortnight ago on a promotional tour for her latest book.
Her sister Joan, 82, who only learned the news herself in the last fortnight, told People magazine she was "completely devastated".
"She was my best friend. I admire how she handled this. She was a wonderful, brave and a beautiful person and I love her," she said.
Jackie Collins, who was born in London, began writing as a teenager, making up racy stories for her schoolfriends, according to a biography on her website.
Her first novel, The World is Full of Married Men, was published in 1968 and became a scandalous bestseller. It was banned in Australia and branded "disgusting" by romance writer Barbara Cartland.
In 1985, her novel Hollywood Wives was made into a mini-series by ABC, starring Anthony Hopkins and Candice Bergen.
Collins said that she "never felt bashful writing about sex". "I think I've helped people's sex lives," she said.
"Sex is a driving force in the world so I don't think it's unusual that I write about sex. I try to make it erotic, too."
Collins had lost her mother, second husband and fiance to cancer.
She told the Press Association earlier this month that she had chosen to celebrate life rather than mourn those she had lost.
"I refuse to mourn people, because everybody dies," she said. "Death and taxes, you can't avoid either".
Private memorial services are due to be held for her family in both the UK and in the US.
The novelist Jackie Collins has died of breast cancer at the age of 77, her family said in a statement.