The 74-year-old, who suffered from Parkinson's Disease, had been admitted to hospital in Arizona on Thursday.
The American boxer won the world championship three times, and was an Olympic gold medallist.
Known as the greatest he was as well known for his fast fists and floating movement as for his fiery character outside of the ring.
President Michael D Higgins is leading tributes to Muhammad Ali here – saying many will remember the wit, grace and beauty he brought to boxing.
Mr Higgins says – as a sportsman and humanitarian – and as someone who struggled for a very long time with one of the most debilitating illnesses – he offered courage in the face of great difficulties.
In 1967 Ali refused to be drafted to fight in Vietnam – he was convicted, stripped of his world title and boxing licence.
Four years later he returned to the sport and fought Al Blue Lewis in Croke Park in 1972.
Olympic Gold medallist Michael Curruth says we'll never see his like again.
