According to news reports, Harrison died at about 1:30 p.m. in a friend's home. His wife, Olivia, and son, Dhani, 23, were at his side.
The news comes just days after reports surfaced that Harrison was in the City of Angels receiving chemotherapy treatment at UCLA Medical Center. Previously, he was reported to have been in a Staten Island hospital undergoing last-ditch experimental radiosurgery for cancer.
While there, he was said to have been visited by longtime friends and former bandmates Paul McCartney and Ringo Starr. McCartney reportedly broke down in tears during what was the final reunion of the three remaining Beatles.
Harrison's family issued a brief statement late Thursday night: "He left this world as he lived in it, conscious of God, fearless of death, and at peace, surrounded by family and friends. He often said, 'Everything else can wait, but the search for God cannot wait, and love one another.' "
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It wasn't immediately known if there would be a public funeral for Harrison. A private ceremony had already taken place, longtime friend Gavin de Becker told the Associated Press.
Harrison had been in failing health for some time. In June, he was treated at a Swiss clinic for a brain tumor, just months after checking into the Mayo Clinic to have surgery on a cancerous lung. He had been battling various forms of the disease for at least three years: In 1998, he underwent radiation therapy for throat cancer, which he attributed to years of smoking.
Despite dire reports of his impending demise this summer, the musician issued an angry statement proclaiming he was alive, well and ready to record again.
In fact, Harrison reportedly headed back to the studio October 1 to record his first new single--and, sadly, his last--since his brain tumor treatment. That final tune, "Horse to the Water," cowritten with Dhani and recorded with British musician Jools Holland, appears on Holland's Small World Big Band, released in Britain on November 19.
With a wink to the increasingly grim news of his health over the past months, and displaying his characteristic dark humor, Harrison credited the song not to his longtime publishing company, Harrisongs, but to "RIP Ltd. 2001."
Given his low-key demeanor, Harrison admitted he never was completely comfortable with the superstar status he achieved with the Beatles. Throughout the years, he fiercely guarded his privacy and was rarely seen in public.
The youngest Beatle, Harrison was born in Liverpool on February 25, 1943. His father, Harold, was a bus driver, and his mother, Louise, a housewife who looked after George and his two brothers and one sister.
It was Harrison's love of guitars and American rockers like Carl Perkins and Chuck Berry that spurred a friendship with an older school chum named Paul McCartney. Paul introduced George to the Quarrymen, a Liverpool band founded by John Lennon. After several lineup changes and a name change, Harrison, Lennon and McCartney brought drummer Ringo Starr aboard. The rest is rock 'n' roll history.
While McCartney and Lennon wrote the bulk of the Beatles' hits, Harrison did have his share of nuggets, including "Taxman," "Something," "Here Comes the Sun" and "While My Guitar Gently Weeps." He also helped introduced Indian culture to pop music, playing the sitar on "Norwegian Wood" and getting the Beatles hooked on Eastern religion.
After the Beatles' breakup in 1970, Harrison was first out of the solo gate with All Things Must Pass, which yielded radio-friendly hits such as "What Is Life?," "If Not for You" and the chart-topping spiritual anthem "My Sweet Lord."
Soon after, Harrison staged the Concert for Bangladesh, a two-day, all-star event held at New York's Madison Square Garden to raise money for the poverty-stricken country. Those shows later became a movie and Grammy-winning live album and served as a model for latter-day megabenefits like Live Aid and the Tibetan Freedom Concert.
Through most of the '80s, little of Harrison's music was commercially or critically embraced. But in 1987, he staged a comeback with the chart-topping Cloud Nine.
A year later, the Beatles were inducted into the Rock and Roll Hall of Fame.
Harrison also cofounded the Traveling Wilburys--a supergroup consisting of Harrison, Bob Dylan, Roy Orbison, Tom Petty and Jeff Lynne. The group's 1988 album, Vol. 1, yielded two hit singles and scored the Wilburys a Grammy.
In the mid 1990s, Harrison returned to his Liverpool roots, reuniting with McCartney and Starr on two unfinished Lennon tracks, "Free as a Bird" and "Real Love." The cuts, part of the comprehensive Anthology project, earned the group three more Grammys to go with their four '60s-era trophies.
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In 1999, a disturbed fan broke into Harrison's suburban London home and stabbed him several times in the chest, puncturing his lung. Harrison eventually recovered; the assailant, 34-year-old Michael Abram, was later acquitted by reason of insanity and remanded to a mental institution.
In September, British health officials issued a formal apology to Harrison, saying they failed to adequately treat Abram and he should never have been released.
Earlier this year, the usually media-shy Harrison made the rounds promoting the 30th anniversary of All Things Must Pass, telling an interviewer: "I had a little throat cancer. I had a piece of my lung removed in 1997. And then I was almost murdered. But I seem to feel stronger...
"[But] I'm a little more short of breath than I used to be, so I don't see myself on stage lasting a full 14 rounds."
Survivors include his second wife, Olivia, his son and bandmates McCartney and Starr.