For six years, latterly with the backing of both houses of a markedly conservative Republican Congress, George Bush has led an American administration that has played an unprecedentedly negative and polarising role in the world's affairs. On Tuesday, in the midterm US congressional elections, American voters rebuffed Mr Bush in spectacular style and with both instant and lasting political consequences. By large numbers and across almost every state of the union, the voters defeated Republican candidates and put the opposition Democrats back in charge of the House of Representatives for the first time in a dozen years.

When the remaining recounts and legal challenges are over, the Democrats may even have narrowly won control of the Senate too. Either way, the results change the political landscape in Washington for the final two years of this now thankfully diminished presidency. They also reassert a different and better United States that can again offer hope instead of despair to the world. Donald Rumsfeld's resignation last night was a fitting climax to the voters' verdict. Thank you, America.

In US domestic terms, the 2006 midterms bring to an end the 12 intensely divisive years of Republican House rule that began under Newt Gingrich in 1994. These have been years of zealously and confrontational conservative politics that have shocked the world and, under Mr Bush, have sent America's global standing plummeting. That long political hurricane has now at last blown itself out for a while, but not before leaving America with a terrible legacy that includes climate-change denial, the end of biological stem-cell research, an aid programme tied to abortion bans, a shockingly permissive gun culture, an embrace of capital punishment equalled only by some of the world's worst tyrannies, the impeachment of Bill Clinton and his replacement by a president who does not believe in Darwin's theory of evolution. The approval by voters in at least five more states of same-sex marriage bans - on top of 13 similar votes in 2004 - shows that culture-war politics are far from over.

Exit polls suggest that four issues counted most in these elections - corruption scandals, the economy, terrorism and Iraq. In the end, though, it was the continuing failure of the war in Iraq that has galvanised many Americans to do what much of the rest of the world had longed for them to do much earlier. It is too soon to say whether 2006 now marks a decisive rejection of the rest of the conservative agenda as well. Only those who do not know America well will imagine that it does.

The Democratic victory was very tight in many places, but its size should not be underestimated. November 7 was a decisive nationwide win for the progressive and moderate traditions in US political life. The final majority in the House will be at least 18. The recapture of the Senate, if it happens, will involve captures from the Republicans in the north-east, the north-west, the midwest and the south. The Democrats won seven new state governorships on Tuesday, including New York and Ohio, and now control a majority nationwide. Republican governors who held on, like Arnold Schwarzenegger in California and Charlie Crist in Florida, only did so by distancing themselves from Mr Bush. The statewide Democratic wins in Ohio give their 2008 presidential candidate a platform for doing what John Kerry failed to do in this crucial state in 2004.

Claire McCaskill's win in the Missouri Senate race showed that Democrats can win a state which almost always votes for the winning presidential candidate. If Jim Webb has won the recounting Virginia Senate seat, Democrats will have gone another step towards re-establishing themselves in a changing part of the south. In almost every one of these cases, as in the Connecticut contest won by Joe Lieberman running as an independent, the Democrats have won by cleaving to the centre and winning the support of independent voters. The new House Speaker Nancy Pelosi may be the Armani-clad San Francisco leftwinger of the caricaturists' dreams but she heads a caucus that will demand caution on some of the baby-boomer liberal generation's pet subjects.

The big questions under the new Congress will be the way that Mr Bush responds to this unfamiliar reduction in his authority and whether the Democratic win will push the president into a new Iraq policy. At his White House press conference yesterday, Mr Bush inevitably made plenty of suitably bipartisan and common-ground noises. He had little alternative. But they rang hollow from such a tarnished and partisan leader. It will take more than warm words in the immediate aftermath of an election reverse to prove that Mr Bush is now capable of working in a new way.

The departure of the disastrous Mr Rumsfeld has come at least three years too late. But it shows that Mr Bush has finally been forced to face the reality of the Iraq disaster for which his defence secretary bears so much responsibility. As the smoke rose over the Pentagon on 9/11, Mr Rumsfeld was already writing a memo that wrongly pointed the finger at Saddam Hussein. He more than anyone beat the drum for the long-held neoconservative obsession with invading Iraq. It was he who insisted, over the advice of all his senior generals, that the invasion required only a third of the forces that the military said they needed. He more than anyone else is the architect of America's humiliations in Iraq. It was truly an outrage that he remained in office for so long.

But at least the passing of Mr Rumsfeld shows that someone in the White House now recognises that things cannot go on as before. Business as usual will not do, either in general or over Iraq. Mr Bush's remarks last night showed that on Iraq he has now put himself in the hands of the Iraq Study Group, chaired by his father's consigliere James Baker, one of whose members, Robert Gates, an ex-CIA chief, was last night appointed to succeed the unlamented Mr Rumsfeld. Maybe the more pragmatic Republican old guard can come to the rescue of this disastrous presidency in its most catastrophic adventure. But it has been the American voters who have at last made this possible. For that alone the entire world owes them its deep gratitude today.