Heavyweight boxing legend Ali said Mandela "taught us forgiveness on a grand scale" as athletes and officials from Australia to Brazil expressed their sadness.
FIFA chief Sepp Blatter called Mandela "one of the greatest humanists of our time" and Tiger Woods said he had been inspired by South Africa's anti-apartheid hero.
Australia and England held a minute's silence before play in the second Ashes cricket Test in Adelaide, a scene replicated by New Zealand and West Indies in Dunedin.
"He made us realise, we are our brother's keeper and that our brothers come in all colours," said Ali, a towering figure in America's civil rights movement.
"What I will remember most about Mr. Mandela is that he was a man whose heart, soul and spirit could not be contained or restrained by racial and economic injustices, metal bars or the burden of hate and revenge.
Blatter, who is attending the 2014 World Cup draw in Brazil, said he and Mandela had "shared an unwavering belief in the extraordinary power of football (and sport generally) to unite people in peace and friendship".
