In a statement, her daughter Melissa said she died surrounded by family and friends, and she thanked hospital staff for their "amazing care".
"My mother's greatest joy in life was to make people laugh," said Melissa Rivers. "Although that is difficult to do right now, I know her final wish would be that we return to laughing soon."
Though far better known for her comedy and TV work than any contribution to cinema – despite providing the voice of Dot Matrix in Mel Brooks' Spaceballs (1987) – Rivers co-wrote and directed Rabbit Test (1978), which helped give Billy Crystal (Analyze This) his big film break and was a considerable achievement for a female filmmaker in male-centric 1970s Hollywood.
Born in Brooklyn in 1933 to Russian immigrants Meyer and Beatrice Molinsky, Joan Alexander Molinsky attended Barnard College, where she graduated with a Bachelor of Arts in English literature. Yet it was her comedy that really caught attention, landed her regular guest appearances on The Tonight Show with Johnny Carson, which in turn led to her status as the shows frequent fill-in host, a stint that ended abruptly when she launched a competing program for Fox.
She went on to host other chat shows, winning awards for The Joan Rivers Show and, more recently, becoming a scathing fixture on red carpets hosting E! Network's Fashion Police where she critiqued fashion and egos with withering power. She wasn't always viewed favourably, coming under fire for her sarcastic take downs of various celebrities and jokes in questionable taste about subjects including the Holocaust, but she always ploughed merrily on regardless. And she had a softer, private side, with friends remembering her as a graceful and kind figure. A prolific author, she wrote several memoirs (including a mock version) and won a Grammy nomination for her comedy album 'What Becomes a Semi-Legend Most?'
US talk show host David Letterman called Rivers "a real pioneer for other women looking for careers in stand-up comedy".
He recalled her guest spots on his show, saying: "She would come out here and sit in this chair and say some things that were unbelievable.
"But it was hilarious... the force of her comedy was overpowering," he added.
On his show, Jimmy Fallon said: "We loved her. We will definitely miss her," while veteran TV interviewer Larry King said: "We will never see her like again."
Comedian and actress Whoopi Goldberg tweeted: "My friend Joan Rivers has passed away once again to quote Billy Crystal... There are no words. Bon Voyage Joan."
TV show host Ellen DeGeneres also described Rivers as a pioneer, adding: "She paved the way for a lot of comedians. I'm very sad she's gone."
Comedian Sarah Silverman said: "My heart is torn in half. She wasn't done."
Kelly Osbourne, who appeared with Rivers on her TV show Fashion Police, said she was "my teacher, therapist, closest friend, inspiration and the only grandmother I ever knew."
The Prince of Wales also paid tribute to Rivers, who attended his wedding to the Duchess of Cornwall in 2005 and performed at a gala for the Prince's Trust on his 60th birthday.
"Joan Rivers was an extraordinary woman with an original and indefatigable spirit, an unstoppable sense of humour and an enormous zest for life. She will be hugely missed and utterly irreplaceable," he said.
In that spirit, then, one last Rivers barb, directed inwards, which is how she would want to be remembered: "I've had so much plastic surgery, when I die they will donate my body to Tupperware."
Our thoughts are with her friends and family.