In Kenya, dozens of new-born babies have been named Obama. In Tehran, an Iranian leader has congratulated a US president-elect for the first time since the Islamic revolution. From Cairo to Kuala Lumpur, Americans abroad have been hugged and congratulated, have cast away their Canadian camouflage and suddenly felt they could walk tall again. The world joined America in its grief seven years ago; now all want to share in America's rejoicing.

Even so, President-elect Obama knows that a difficult inheritance awaits him overseas. US forces are engaged in two wars, and Afghanistan at least is proving a harsh challenge. Pakistan stands on the brink of disaster. Iran, the Palestinian-Israeli conflict, massacres in the Congo and Russia's belligerence all demand skilful diplomacy and determined leadership in the White House. None of these, however, will be the priority for the incoming president. His first task must be to use the goodwill created by his election to restore confidence in America.

There are actions he can, and probably will, take swiftly: closing Guantanamo, signing the UN Convention against Torture, discarding lingering US scepticism over climate change, announcing fresh budgetary support for the United Nations. Such measures would win respect and popularity abroad and would be seen as a harbinger of a new readiness for inclusive, co-operative diplomacy. Mr Obama may find that such an end to American exceptionalism would be welcomed even at home: many US voters have been hurt by the world's criticisms of the Bush Administration and have resented its policies that have left them isolated and unpopular.

The mechanism for change is already in place. For the past eight years the State Department, one of the world's greatest repositories of diplomatic skill and intelligence, has been kept at arm's length. Its advice has been ignored, its counsels mocked by ideologues in the White House who saw only appeasement and liberalism in Foggy Bottom. Colin Powell was often a lone voice, and embattled diplomats abroad had one hand tied behind their backs.

Changing the tone of diplomacy does not immediately change the content. There will still be intractable issues. But tone matters. Instead of rejecting proposals simply because they came from the Bush Administration, many countries will be looking for ways to support an Obama presidency. That can greatly ease the search for solutions. Anti-Americanism will not disappear. But whereas George Bush became an excuse to legitimise this ugly trait, the next president can again make it an aberration. When America is inspiring, people everywhere are willing to be inspired.

President-elect Obama now has a singular opportunity to show what he means by a “new dawn of leadership” and end a transatlantic divide that has been as bad for the things in which Europeans believe as it has been bad for the US. One of the great casualties of the past eight years had been the Western alliance. Mr Obama's first visit should therefore be to Europe. Here the values and ambitions of the West are genuinely challenged - not only by a resurgent Russia but also by a cynical public. Europeans must themselves make the most of the new beginning. Crowds even larger than those who greeted him in Berlin will surely come out to welcome him.