President Bush said today that all Americans could take pride in the election of Barack Obama no matter which candidate they backed in an election that had left America "a more perfect union".

Mr Bush delivered his tribute from the gardens of the White House as Mr Obama hunkered down at home in Chicago to choose the men and women that will accompany him to Washington in January.

After a landslide victory that saw him chosen as America's first black president, Mr Obama knows that there is no time to lose if he wants to build an administration to extricate the US military from Iraq and deliver the change he promised to voters.

As he told more than 100,000 supporters packed into Chicago's Grant Park for his victory rally last night: "We know the challenges that tomorrow will bring are the greatest of our lifetime: two wars, a planet in peril, the worst financial crisis in a century."

The first pick on his team sheet – to be officially confirmed later today – is Rahm Emanuel, the combative but highly effective Chicago congressman who advised Bill Clinton in the 1990s. Mr Emanuel – known as 'Rahmbo' – has agreed to return to the White House as chief of staff.

Other posts likely to be filled within days include Treasury Secretary, Secretary of State and Defence Secretary - even though Mr Obama will not be sworn in as the 44th President of the United States until January.

Mr Bush said today that he wanted the transition to be as smooth as possible – and the divisions that have marked the campaign to be forgotten.

“It will be a stirring sight to watch President Obama, his wife Michelle, and their beautiful girls step through the doors of the White House,” Mr Bush said.

“I know millions of Americans will be overcome with pride at this inspiring moment that so many have awaited so long. I know Senator Obama’s beloved mother and grandparents would have been thrilled to watch the child they raised ascend the steps of the Capitol - and take his oath to uphold the Constitution of the greatest nation on the face of the earth.”

The President said he had invited the Obamas to visit him in the White House “as soon as possible”.

“No matter how they cast their ballots, all Americans can be proud of the history that was made yesterday,” he declared.

“Across the country, citizens voted in large numbers. They showed a watching world the vitality of America’s democracy, and the strides we have made towards a more perfect union. They chose a president whose journey represents a triumph of the American story - a testament to hard work, optimism, and faith in the enduring promise of our nation.

“Many of our citizens thought they would never live to see that day. This moment is especially uplifting for a generation of Americans who witnessed the struggle for civil rights with their own eyes - and four decades later see the dream fulfilled.”

He added: “A long campaign has now ended, and we move forward as one nation. We’re embarking on a period of change in Washington, yet there are some things that will not change. The United States government will stay vigilant in meeting its most important responsibility - protecting the American people. And the world can be certain this commitment will remain steadfast under our next commander-in-chief.”

Political experts agreed on the need for a smooth handover of power. “The need for a seamless transition is greater than it has been in our adult political lifetime,” said William Galston, a former Clinton adviser who is now a professor at the University of Maryland. “With two wars abroad and an international financial crisis going on, there cannot be a period in which the new administration is just getting up to speed."

To ensure that does not happen, top intelligence officials will start giving Mr Obama daily classified security briefings from tomorrow. Even during his campaign, his aides worked on a transition strategy to allow him to switch out of campaign mode without fuss.

As Obama fans around the world celebrated his success on the beaches of Brazil and the boulevards of Berlin - and their leaders lined up to offer their congratulations - the first signs were already emerging of the challenges he will face in office.

Among those foreign leaders offering their congratulations was Hamid Karzai, the US-backed President of Afghanistan, who noted claims that dozens of women and children had been killed in a US airstrike on Monday that hit a wedding party in the province of Kandahar.

"We cannot win the fight against terrorism with airstrikes,” Mr Karzai said. “This is my first demand of the new President of the United States - to put an end to civilian casualties.”

There was also sabre-rattling by the Russian President, Dmitry Medvedev who used his first annual address to parliament to launch a stinging attack on US policy and announce the Kremlin was to station new missiles near the Polish border in response to US plans for an anti-missile system.

“I would like to stress: we have no problems with the American people. We have no innate anti-Americanism,” Mr Medvedev said. “We hope that our partners – the new US administration – will make a choice in favour of fully-fledged relations with Russia."

Times Recommends

• Rio Tinto four held as China prepares case
• Diplomats must keep heads down and trousers up
• When in Rome should one make like Berlusconi?