The former world heavyweight boxing champion, one of the world's best-known sportsmen, died at a hospital in the US city of Phoenix in Arizona state after being admitted on Thursday.
He was suffering from a respiratory illness, a condition that was complicated by Parkinson's disease.
The funeral will take place in Ali's hometown of Louisville, Kentucky, his family said in a statement.
Born Cassius Marcellus Clay, Ali shot to fame by winning light-heavyweight gold at the 1960 Rome Olympics.
Nicknamed "The Greatest", the American beat Sonny Liston in 1964 to win his first world title and became the first boxer to capture a world heavyweight title on three separate occasions.
He eventually retired in 1981, having won 56 of his 61 fights.
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