![image: [ Frank Sinatra - as he will always be remembered ]](/olmedia/90000/images/_94141_sinatra_300.jpg)
His publicist Susan Reynolds said he died in the emergency room of Cedars-Sinai Medical Center.
Barbara, Sinatra's wife of 20 years, and other family members were with him when he died, she added.
The spokeswoman said a private funeral was planned.
Sinatra has not been seen in public since a heart attack in January 1997, and had been in and out of the hospital several times since then.
His family had occasionally acknowledged he was ill but denied rumours that he was on his death bed.
Regular updates by the Sinatra family on their Website, including photographs of the singer enjoying himself, helped show that he was battling on.
In February the family used the Internet site to deny rumours that the star had inoperable cancer after he was taken to hospital for a series of tests amid reports that he had cancer of the bladder.
American author Gore Vidal told BBC Radio 4's Today programme that the singer had played a unique part in the life of his country.
He said: "I would say that half the population of the United States over the age of 40 were conceived while their parents were listening to his records.
"He played a great romantic role in the country."
Country singing star Kenny Rogers said: "When I first got started in this business I made all my decisions thinking `Was this something Sinatra would do?'"
Sinatra's last months were dogged by rumours of a battle between his fourth wife Barbara and the three children from his first marriage over how his fortune - estimated at £124m ($200m) - should be split.
The star was first married to Nancy Barbato, whom he met as a teenager in Long Island, New Jersey. They divorced after 11 years in 1950. He later married actresses Mia Farrow and Ava Gardner.
The crooner, nicknamed Ol' Blue Eyes, was the son of Italian immigrants and started entertaining as a singing waiter.
He rose to become one of the world's richest and most loved singers. He also became a movie star, appearing in a series of films including "From Here to Eternity", for which he won an Oscar.
But it was his classic songs, "My Way", "Strangers in the Night" and "New York, New York", that most people will forever associate him.
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Farewell to Ol' Blue Eyes
(15 May 98 | Special Report)
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Frank Sinatra dies aged 82
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Screams to big screen idol
(15 May 98 | World)
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