Ali, a three-time world heavyweight champion and civil rights activist who was an iconic figure of the 20th century, died Friday aged 74 after health problems complicated by a long battle with Parkinson's disease.
The official cause of death was septic shock due to unspecified natural causes.
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The dazzling fighter -- whose words, often delivered in catchy rhymes, were as devastating as his punches -- had been admitted to an Arizona hospital earlier in the week.
Political leaders, sports figures, celebrities and fans around the world paused to remember "The Greatest," whose career spanned three decades.
On Sunday, Ali's relatives will accompany his body from Scottsdale, Arizona to Louisville, his hometown in the southern state of Kentucky.
After a private family funeral on Thursday, Ali's coffin will be transported through the streets of Louisville on Friday, before a public memorial service at an arena, with former president Bill Clinton among celebrities expected to offer eulogies.
The procession has been organized to "allow anyone that is there from the world to say goodbye," family spokesman Bob Gunnell told reporters.
Louisville lowered flags to half-staff in his honor, as fans flocked to the boxer's modest childhood home, now a museum, to pay their respects.
"Our hearts are literally hurting. But we are happy daddy is free now," Ali's daughter Hana Ali wrote on Twitter.
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President Barack Obama led tributes for Ali, issuing an unusually personal statement in which he said he keeps a pair of Ali's boxing gloves and a photo in his private study.
"Muhammad Ali was The Greatest. Period," Obama said.
"His fight outside the ring would cost him his title and his public standing. It would earn him enemies on the left and the right, make him reviled and nearly send him to jail. But Ali stood his ground," Obama said.
Obama later called Ali's widow Lonnie to offer condolences, the White House said.
In a possible preview of Bill Clinton's eulogy, he and his wife Hillary, who is seeking the Democratic presidential nomination, said Ali was "a blend of beauty and grace, speed and strength that may never be matched again."
Ali was hospitalized in the Phoenix area early this week, but his condition quickly deteriorated.
"His final hours were spent with just immediate family," Gunnell said. "He did not suffer."
Ali had been living in the Phoenix area with Lonnie, his fourth wife whom he married in 1986. He was survived by nine children -- seven daughters and two sons.
The fighter himself planned much of the memorial events, Gunnell said.
The interfaith service is to be conducted at Louisville's KFC Yum! Center in accordance with "Muslim tradition" and in the presence of an imam.
Ali will be buried at Cave Hill Cemetery in Louisville, where he was born in 1942.
Outside the family home in Louisville and the hospital in Scottsdale, fans left flowers, letters and mementos.
"He just represents everything that was good about mankind and it's sad to see him go," said James Brice.
Fans also gathered in Los Angeles to snap photos and leave flowers at Ali's star on the Hollywood Walk of Fame.
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Ali had been hospitalized multiple times in recent years.
His Parkinson's had limited his public speaking, but Ali continued to make appearances and statements via his entourage.
Ali's career stretched from 1960 to 1981 and he retired with a record of 56-5, including such historic bouts as the "Rumble in the Jungle" against George Foreman.
Don King promoted that watershed bout in Kinshasa, Zaire, in 1974, in which Ali used his "Rope a Dope" strategy to best Foreman and become just the second fighter ever to regain the heavyweight world title.
"He hit me with a quick one-two, knocked me down to the canvas and my whole life changed," Foreman told CNN of the epic "Rumble."
"I was devastated," he said. "Little did I know I would make the best friend I ever had in my life."
Other defining moments of Ali's career included two knockouts of Sonny Liston and his rivalry with Joe Frazier.
King said that Ali's "spirit will go on forever. He represents what every athlete and sports person tries to do, an attitude of getting it done, success."
Ali -- born Cassius Marcellus Clay Jr on January 17, 1942 -- dazzled fans with slick moves in the ring and his wit and engaging persona outside it.
He famously said he could he "float like a butterfly, sting like a bee" in the ring.
He took the name of Muhammad Ali after converting to Islam in 1964, soon after he had stunned the sport by claiming the world title with a monumental upset of Liston.
Ali's refusal to serve in the Vietnam War saw him prosecuted for draft evasion, and led to him being effectively banned for boxing for three years of his prime. The US Supreme Court overturned his conviction for draft dodging in 1971.
Ali held firm to his beliefs and eventually earned accolades as a civil rights activist.
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He received the highest US civilian honor, the Presidential Medal of Freedom, in 2005 and was chosen to light the Olympic torch in 1996, his hands trembling due to Parkinson's -- a poignant moment for the sports world.
Celebrities, politicians, athletes and reporters who covered his career praised Ali for his superb work in and out of the ring.
Floyd Mayweather, who retired from boxing last year with a perfect 49-0 record, was in awe when met Ali in 1996.
Twenty years on, Mayweather summarised Ali's legacy.
"Never be afraid," Mayweather said. "Never stop believing. And never settle for less."
Mayweather's great rival Manny Pacquiao of the Philippines said the world had lost "a giant."
"Boxing benefited from Muhammad Ali's talents, but not as much as mankind benefited from his humanity," Pacquiao said.
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