Melissa Rivers, the comedian's only child, said her mother died peacefully, surrounded by family and friends, at 1:17 p.m. EDT (1717 GMT).
"My mother's greatest joy in life was to make people laugh. Although that is difficult to do right now, I know her final wish would be that we return to laughing soon," Melissa Rivers added in a statement.
There were no immediate details about a funeral or memorial service.
Rivers was the second leading American comedian to die in less than a month. Groundbreaking comedy star and actor Robin Williams, 63, hanged himself on Aug. 13 in California.
As news of her death spread, photographers, reporters and television crews gathered outside the hospital where Rivers died, and fans placed bouquets of flowers at the entrance to her apartment on Manhattan's Upper East Side.
The Brooklyn-born comedian, who once described herself as "the plastic surgery poster girl" and often joked about her numerous cosmetic enhancements, suffered cardiac arrest during a procedure on her vocal cords at a Manhattan clinic on Aug. 28. She was rushed to Mount Sinai Hospital, where she was put on life support.
A spokeswoman for the Medical Examiner's Office in New York said it is investigating the cause and manner of Rivers's death on Thursday. She did not specify when the autopsy on Rivers would take place and when results would be released.
Friends and fellow comedians on Thursday expressed their grief and sadness and praised Rivers.
"No one loved life, laughter, and a good time more than Joan. We would have dinner and laugh and gossip and I always left the table smiling," said journalist Barbara Walters.
"She was a brassy, often outrageous, and hilarious performer," she added in a statement.
Israeli President Benjamin Netanyahu expressed his condolences to Rivers's family and said she would be deeply missed.
"Joan Rivers brought laughter to millions around the world and was proud of her Jewish heritage and a vocal supporter of the State of Israel," he said in a statement.
The New York State Department of Health also said Thursday it is investigating the comedian's death. A telephone message seeking comment from the clinic where Rivers was treated was not immediately returned.
Earlier this week, a representative for Rivers said media reports that her family was planning to sue the clinic were not true.
Among others praising and remembering Rivers was actress Liza Minnelli who described her as a dear friend.
"I will always remember the laughter and friendship she brought into my life," she said in a posting on Facebook.
Comedian Louis C.K. praised Rivers's talent and genius. "I never saw someone attack a stage with so much energy. She was a controlled lightning bolt," he said in a statement.
Property mogul Donald Trump, who hosted the reality TV competition show "The Apprentice," which Rivers won in 2009, described her as "an amazing woman and a great friend."
"Her energy and talent were boundless. She will be greatly missed," he added on Twitter.
Joan Alexandra Molinsky was born on June 8, 1933, in Brooklyn and grew up there and in a nearby town, the daughter of a doctor and a housewife. The Barnard College graduate began pursuing an entertainment career with the last name Rivers, which she borrowed from her agent.
Her lengthy career included stand-up comedy, television, writing and an Emmy Award-winning daytime talk show, "The Joan Rivers Show." But she originally wanted to be an actress.
She got into comedy after writing sketches for television's "The Ed Sullivan Show." A career in stand-up followed. She later worked as a regular guest host for Johnny Carson on NBC's "The Tonight Show."
When she started her own late-night talk show in 1986, on the rival Fox network, it caused a falling-out with Carson that lasted until he died in 2005. Rivers's show was canceled after seven months due to low ratings.
A few months later, her husband and manager, Edgar Rosenberg, committed suicide and Rivers fell into depression.
Later in her career, Rivers and her daughter starred in the reality TV show "Joan & Melissa: Joan Knows Best", with Rivers living with her grown child.
Most recently, Rivers was the host of cable television channel E!'s "Fashion Police," commenting on the unfortunate red carpet choices of Hollywood celebrities.
Actress Anna Kendrick, a target of the comedian's barbed comments, said she will be truly missed.
"RIP Joan Rivers. Being publicly told that my dress is hideous will never feel quite as awesome," she tweeted.