Incumbent has been granted four more years to make good on early hopes.
America has chosen and the world will be the better or worse for it. Anyone who doubts that a presidential election makes much difference to the course of events has already forgotten the first election of the 21st century. If a few hundred votes in Florida had gone the other way in 2000, there would have been no invasion of Iraq, the US response to 9/11 would have been different, and the world's response to climate change might have been more co-ordinated and well advanced by now.
It is harder to predict the consequences of the choice Americans made yesterday. President Obama had to run on his management of the economy, reminding the country of the mess he inherited and the steps he had taken to preserve the car industry and protect jobs generally. His re-election suggests a continuation of the slow recovery, but might he do more?
His first economic challenge is the "fiscal cliff" looming next month when tax cuts expire and spending reductions must be made. Together those measures would take money out of an economy still struggling to recover from the recession four years ago.
With the authority of his re-election, Mr Obama's hand should be strengthened in negotiations with the outgoing Congress. It will probably agree to extend the tax cuts and maintain present spending levels. But the President ought to be thinking further ahead. The election campaign was tougher than he thought it was going to be. Mitt Romney struck a chord with criticism of his economic leadership.
Business needs to see beyond the fiscal and monetary stimulants that have sustained activity since the global financial crisis. Mr Obama should quickly indicate when taxes will be increased and spending contained.
A second-term president has no need to worry about another election. He has four years to do what he believes to be the right thing for the country. Mr Obama already has a notable achievement in healthcare; his re-election is the endorsement his programme needed and surely puts it beyond further debate. He might dare now to turn to other social problems, particularly those of poor and largely black urban communities lacking employment and family stability.
The symptoms of those problems are drugs and street crime. The election of a black president not once but twice ought to be doing something to reduce the country's racial divide and the fear it generates.
The re-elected President might turn his attention to the proliferation of firearms that have brought more atrocities to the US than the country has suffered from external terrorism.
He might also give greater attention to the Middle East in a second term. He needs to act more decisively against Israeli settlement of the occupied territories and encourage Palestinian factions to unite for resumed negotiations for their own state.
His re-election means US relations with China will be better than they might have been under his rival. Asia and the Pacific are better known to Mr Obama and multilateral trade negotiations towards the Trans-Pacific Partnership will proceed in New Zealand next month.
Continuity in government is usually to be welcomed. President Obama has been given four more years to fulfil the high hopes he once encouraged. He needs to strengthen his team with new appointments and put himself out front more often, giving better leadership to America and the world.