Ali, born as Cassius Marcellus Clay, died in a Phoenix hospital after being admitted for a respiratory infection.
The former heavyweight boxer, aged 74, has been suffering Parkinson's disease for more than three decades now.
His funeral, the family says, will be held in his hometown of Louisville, Kentucky.
Nicknamed 'The Greatest', Ali shot to fame after winning Gold in light-heavyweight boxing at the 1960 Olympics.
He went on to fight 61 times, winning 56 of them. He retired in 1981.
'Return to the Fatherland'
Ali visited Ghana in 1964 during the reign of Osagyefo Dr Kwame Nkrumah, the country's first president.
He called that visit 'A Return to the Fatherland'.
Ali is rumoured to have fathered Houston-based Ghanaian Kiiursti Mensah Ali with one Barbara Mensah. Kiiursti is believed to be the 10th child of the legend.
'The Return to the Fatherland'
As a poet, Ali was popular in his pre- and post-fight talks.
In his legendary fight with George Foreman in modern DR Congo in 1974 in what was dubbed 'Rumble in the Jungle', Ali made one of his popular statements: 'Float like a butterfly, sting like a bee. your hands can't hit what your eyes can't see'.
By Emmanuel Kwame Amoh|tv3network.com|Ghana