The award-winning star had been in Mount Sinai Hospital since August 28, when she reportedly stopped breathing during a medical procedure on her vocal cords at a clinic in New York.
"It is with great sadness that I announce the death of my mother, Joan Rivers. She passed peacefully at 1:17 pm surrounded by family and close friends," daughter Melissa Rivers said.
Melissa and grandson Cooper had kept a vigil at Rivers' bedside since flying in from Los Angeles as soon as she fell ill.
"My mother's greatest joy in life was to make people laugh," her daughter added. "Although that is difficult to do right now, I know her final wish would be that we return to laughing soon."
Celebrities, including many younger female comics who followed her onto stages once dominated by men, raced to pay tribute to her rapier wit as their inspiration and to express their condolences.
"There are no words. Bon Voyage Joan," tweeted Oscar-winning actress and comic Whoopi Goldberg.
"A legend, a friend, a mentor, an icon, and wildly funny. One of a kind. RIP," said fellow comic Kathy Griffin, tweeting a picture of herself with Rivers.
"Rest in peace, Joan. We will always love you," said country music star Dolly Parton.
In Los Angeles, a scrum of tourists and journalists gathered at Rivers' star on the Hollywood Walk of Fame where flowers were laid.
Dan Shadbolt, 43, who was visiting from Britain with his wife and three kids, said: "It's terrible news. She was an icon for me."
Israeli Prime Minister Benjamin Netanyahu extended heartfelt condolences for the loss of a comedy icon who brought laughter to millions around the world and was a vocal supporter of Israel.
- 'Can we talk?' -
New York State Health Department said it was investigating the circumstances that surrounded her reported cardiac arrest while she was an outpatient at Yorkville Endoscopy Center.
The daughter of a well-off, middle-class Jewish family, Rivers enjoyed a stunningly successful career that lasted decades and worked right up until falling ill last week.
Born Joan Alexandra Molinsky in Brooklyn, she graduated from New York's Barnard College and worked in the fashion industry before starting out in stand-up under the stage name Joan Rivers.
She spared no one her razor-sharp wit and was considered one of the best at delivering a cutting one-liner, and perhaps the most foul-mouthed of a breakthrough generation of US "comediennes".
She took aim at celebrities and public figures, joking about modern America's obsession with image and neuroses.
Her signature catch phrase was "Can we talk?" -- an icebreaker she used before verbally drop-kicking the object of her ridicule.
She told an interviewer that she thought it up while on the stand-up circuit in Las Vegas during the 1980s.
The joke at the time, she said, "was probably about Elizabeth Taylor being fat, and people gasped and I went, 'Can we talk here?'
"What you’re really saying is, 'Come on, are we going to talk the truth?'"
Tough and tenacious, she supported herself for years with secretarial work while doing comedy gigs, until she got her big break on the popular "Tonight Show" program in 1965.
Four months after landing a regular gig, she married one of the show's producers Edgar Rosenberg. They had Melissa in 1968.
Rivers used to say that no subject was off-limits in her comedy: not even her husband's suicide in 1987.
"That's how I get through life. God has given us this gift of humor," she told New York Magazine. "Animals don't laugh."
In her 2013 book "I Hate Everyone... Starting With Me," Rivers joked about her own funeral, saying she wanted "a huge showbiz affair" with Meryl Streep "crying in five different accents."
But she also sparked controversy over the years with outspoken remarks on the Middle East and, on one occasion, when the butt of her humor was the survivors of the 9/11 terror attacks.
In later years, Rivers became as well-known for her love of plastic surgery, taken to excess with her exaggerated cheek bones and her preternaturally wrinkle-free face.
She reinvented herself as the host of "Fashion Police," a show that offered running critiques of the red carpet attire worn by the glitterati at the Oscars and other A-list events.
Rivers, who admitted to being a workaholic, said she hoped never to have to cede the stage.
"I'm an addict. It's my drug. I love my work, This is where I'm happiest," she once said.
US media reported that her funeral would be held on Sunday at Temple Emanu-El synagogue in New York.