Confirmation of Ali's death, at the age of 74, prompted an understandable outpouring of emotion on Saturday, with the likes of Pele, Tiger Woods and Sachin Tendulkar among countless sporting stars quick to salute the former heavyweight world champion.
However, Ali was a man who transcended sport - as evidenced by the moving statement issued by Obama, who was fulsome in his praise of "The Greatest. Period."
Obama wrote: "In my private study, just off the Oval Office, I keep a pair of his gloves on display, just under that iconic photograph of him - the young champ, just 22 years old, roaring like a lion over a fallen Sonny Liston.
"I was too young when it was taken to understand who he was - still Cassius Clay, already an Olympic gold medal winner, yet to set out on a spiritual journey that would lead him to his Muslim faith, exile him at the peak of his power, and set the stage for his return to greatness with a name as familiar to the downtrodden in the slums of Southeast Asia and the villages of Africa as it was to cheering crowds in Madison Square Garden.
"'I am America,' he once declared. 'I am the part you won't recognise. But get used to me - black, confident, cocky; my name, not yours; my religion, not yours; my goals, my own. Get used to me'.
"That's the Ali I came to know as I came of age - not just as skilled a poet on the mic as he was a fighter in the ring, but a man who fought for what was right. A man who fought for us. He stood with [Martin Luther] King and [Nelson] Mandela; stood up when it was hard; spoke out when others wouldn't. His fight outside the ring would cost him his title and his public standing. It would earn him enemies on the left and the right, make him reviled, and nearly send him to jail. But Ali stood his ground. And his victory helped us get used to the America we recognise today.
"He wasn't perfect, of course. For all his magic in the ring, he could be careless with his words, and full of contradictions as his faith evolved. But his wonderful, infectious, even innocent spirit ultimately won him more fans than foes - maybe because in him, we hoped to see something of ourselves.
"Later, as his physical powers ebbed, he became an even more powerful force for peace and reconciliation around the world. We saw a man who said he was so mean he'd make medicine sick reveal a soft spot, visiting children with illness and disability around the world, telling them they, too, could become the greatest.
"We watched a hero light a torch [at the 1996 Atlanta Olympics], and fight his greatest fight of all on the world stage once again; a battle against the disease that ravaged his body, but couldn't take the spark from his eyes.
"Muhammad Ali shook up the world. And the world is better for it. We are all better for it. Michelle and I send our deepest condolences to his family, and we pray that the greatest fighter of them all finally rests in peace."
Former US president Bill Clinton also hailed Ali, stating: "We watched him grow from the brash self-confidence of youth and success into a manhood full of religious and political convictions that led him to make tough choices and live with the consequences.
"Along the way we saw him 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.
"I was honoured to award him the Presidential Citizens Medal at the White House, to watch him light the Olympic flame, and to forge a friendship with a man who, through triumph and trials, became even greater than his legend."