President Karzai met UN chief Ban Ki-moon earlier in the day
Hamid Karzai has been declared president of Afghanistan, after election officials scrapped a planned second round of voting.
The announcement comes a day after Mr Karzai's sole challenger, Abdullah Abdullah, pulled out of the race.
Dr Abdullah, who had demanded the removal of key poll officials, said the vote would not have been fair. The first round had been marred by fraud.
The US responded by saying Mr Karzai was Afghanistan's "legitimate leader".
White House spokesman Robert Gibbs said President Barack Obama would telephone Mr Karzai shortly.
Andrew North, BBC News, Kabul
The announcement that the run-off vote was being cancelled had been widely expected. All reports suggested it was simply a question of finding the legal means to bring the process to an end.
The point of holding a second round was to try to restore some legitimacy to the process after there was so much fraud - almost a third of votes for President Karzai were invalidated because of massive ballot stuffing.
Now the second round has been cancelled, largely because of international pressure. It is a very unsatisfactory end, not the end anyone here wished for. At the moment it is being seen as the best of a lot of bad options.
But some questions are bound to remain over the legitimacy of the whole process.
On Monday a spokesman for the Independent Election Commission (IEC), Azizullah Lodin, declared that President Karzai, "the only candidate for the second round", had been "elected president of Afghanistan".
He said the second round on 7 November was being scrapped to save money, for security reasons and to prevent further setbacks that could damage Afghanistan politically and economically.
The Taliban, which carried out attacks across the country during the first round, had vowed to disrupt the polls again next Saturday.
President Karzai - who was first elected Afghan president in 2004 - had been the favourite to win another five-year term in the run-off.
One of the reasons for holding a deciding vote had been to try to restore some legitimacy to the process, after the discredited first round on 20 August.
A number of international figures, including US Senator John Kerry, US Secretary of State Hillary Clinton and UK Prime Minister Gordon Brown, had been involved in persuading Mr Karzai to accept a run-off.
However, Mr Brown on Monday said he welcomed the commission's decision.
The Independent Election Commission announces Mr Karzai's election
A spokesman said the PM had "spoken to President Karzai to congratulate him on his re-election" and the two men had "discussed the importance of the president moving quickly to set out a unifying programme for the future of Afghanistan".
The US administration, through its embassy in Kabul, also hailed the commission's move, which it said conformed to "its mandate under Afghan law".
The statement added: "We congratulate President Karzai on his victory in this historic election and look forward to working with him."
Earlier on Monday, UN Secretary General Ban Ki-moon visited Kabul and said Afghanistan's troubled election had been among "the most difficult the United Nations has ever supported".
The BBC's Lyse Doucet in Kabul says there had been intense discussion in recent days as to whether scrapping the second round would be constitutionally legal.
Some observers are saying Mr Karzai's legitimacy is also in question, and ask whether his government can be effective, adds our correspondent.
This would be a particular concern to President Obama as he considers whether to send up to 40,000 more troops to Afghanistan.
Hundreds of thousands of votes were discounted from August's first round, including almost a third of ballots cast for Mr Karzai.
The incumbent's share of the vote was cut to just under the crucial 50% plus one ballot threshold needed for outright victory, following an investigation by the UN-backed Electoral Complaints Commission.
Dr Abdullah had demanded key officials be removed from the IEC, which is widely regarded as pro-Karzai, ahead of any run-off vote.
Dr Abdullah - a Tajik-Pashtun former eye surgeon and ex-foreign minister - was adjudged in the end to have won nearly a third of valid votes cast.
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