He had been suffering from a respiratory illness, a condition that was complicated by Parkinson's disease.
"Muhammad Ali shook up the world. And the world is better for it," said US President Barack Obama and his wife Michelle.
Former President Bill Clinton - husband of Democratic frontrunner Hillary - said the boxer had been "courageous in the ring, inspiring to the young, compassionate to those in need, and strong and good-humoured in bearing the burden of his own health challenges".
Republican presumptive presidential nominee Donald Trump, meanwhile, tweeted that Ali was "truly great champion and a wonderful guy. He will be missed by all!"
Muhammad Ali
Born Cassius Marcellus Clay, 17 January 1942
61 fights
over a professional career lasting 21 years
56 wins
including 37 knockouts
·
3 times crowned
World Heavyweight Champion
·
1
Light-heavyweight Olympic gold medal
·
31 straight wins
before being beaten by Joe Frazier
Ali's funeral will take place in his hometown of Louisville, Kentucky, said his family.
Tributes for the heavyweight great have been pouring in from across the world.
George Foreman, who lost his world title to Ali in the famous "Rumble
in the Jungle" fight in Kinshasa in 1974, called him one of the greatest
human beings he had ever met. Ali's funeral will take place in his hometown of Louisville, Kentucky, said his family.
Tributes for the heavyweight great have been pouring in from across the world.
American civil rights campaigner Jesse Jackson said Ali had been willing to sacrifice the crown and money for his principles when he refused to serve in the Vietnam war.
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