When the moment came, TV panellists who had talked volubly all evening suddenly found it hard to say a word. In Grant Park, Chicago, Jesse Jackson wept. Nearby, an assemblyman from the Illinois black caucus was asked what the election meant for him. “Now I can look my grandchildren in the eye,” he said simply. “And I can tell them, if they want to, they can be president, too.”

On Tuesday night, with a countdown to precisely 10pm Chicago time, American democracy transformed in an instant not only the hopes and expectations of African Americans, but also the self-image of their country and their country’s image in the world.

Barack Obama stepped out to accept his city’s rapturous acclaim a few minutes later. “If there is anyone out there who still doubts that America is a place where all things are possible . . .” he began, but at that moment it seemed no one did doubt it — anywhere. Bedlam had already taken hold in cities across the US, in Berlin, where Senator Obama drew a crowd of 200,000 when merely a candidate, and from Japan to Kenya, where his extended family now awaits their invitation to the inauguration.

Within hours Gordon Brown and David Cameron were vying in the House of Commons for scraps of the President-elect’s reflected glory. In Moscow, by contrast, in an 85-minute state-of-the-nation address, President Medvedev made no mention of the US election. Small wonder. Nothing is more alarming to the stage managers of phoney democracies than the sight of real ones sweeping entire political classes from the stage in a day of bloodless voting.

By the same token, nothing is more inspiring for ordinary citizens. One in 50 people on the planet voted in this election, but it was truly a global political event. This is not just because of the openness of the American electoral system and of its voters’ yearnings. It is not just because of the theatricality of the marathon campaigns, or because, despite its soaring deficits and disastrous loss of prestige in the Iraq war, the US remains the most powerful nation on earth.

The world has been fascinated and profoundly moved by this election most of all because of what America is — a nation founded on universal aspirations, and thus a mirror to humanity. For two centuries that mirror has seemed irreparably cracked by the legacy of slavery and segregation, a pernicious and enduring racism that remains a factor in the blighted lives of so many of the poor blacks among whom Mr Obama launched his political career. He is not the last role model they will ever need, but he is the most powerful proof his country has produced that it is ready to judge them by the content of their character, not the colour of their skin.

The delirium in Grant Park came mainly from the young, diverse, tech-savvy America that gave the Obama campaign many of its footsoldiers and much of its money. A very different America had gathered on the great lawn of the Arizona Biltmore. The Phoenix Boys’ Choir, in immaculate blue blazers, sang for miserable McCain campaign staff who turned off their big-screen TVs to be able to ignore the networks’ mounting evidence of defeat.

When Senator McCain conceded, he had to silence booing prompted by his rival’s name. But he did so in a speech of enormous grace and humility that conveyed not only his respect for the democratic process, but his understanding that in the manner of his losing the election he was helping to make history.

Yesterday President Bush called this election “a triumph of the American story”. It has been exactly that. America may have faltered in its efforts to export democracy, but this time, at home, it has delivered a masterclass in the real thing.