News of the run-off vote follows weeks of mounting international pressure.
It comes a day after a UN-backed panel said it had clear evidence of fraud in August's first round, lowering Mr Karzai's vote share below 50%.
Mr Karzai told a news conference that he accepted the findings, adding they were a "step forward" for democracy.
Initial results suggested Mr Karzai, the incumbent, had received 55% of the vote, and ex-Foreign Minister Mr Abdullah 28%.
But the UN-backed Electoral Complaints Commission (ECC) ordered that ballots from 210 polling stations be discounted.
This meant Mr Karzai's total was reduced to below the 50% plus one vote threshold for outright victory, indicating a second round was needed.
Since the disputed first round of polling, there has been intensive Western lobbying of Afghanistan's leaders to resolve the weeks of political paralysis.
The White House - debating a request for 40,000 more US troops to be sent to Afghanistan - warned at the weekend no more soldiers would be deployed until a political resolution was reached.
Correspondents say it was therefore not surprising to see Mr Karzai give his reaction to the run-off, at a news conference alongside UN envoy Kai Eide and US Senator John Kerry.
"This is not the right time to discuss investigations, this is the time to move forward to stability and national unity," Mr Karzai said.
"I call upon our nation to change this into an opportunity to strengthen our resolve and determination, to move our country forward and to participate in the new round of elections."
Fazel Sangcharaki, spokesman for Dr Abdullah Abdullah, said: "We had hoped the president would accept the second round and we are ready and fully prepared for a second round."
The BBC's Martin Patience, in Kabul, says there will be concerns about the logistics of a second vote - about getting ballots out into the provinces and also about the security situation.
There will also be absolutely no guarantee that any new vote will be free of the fraud that dogged the first round, our correspondent says.
But for now the political deadlock appears to have been broken, for a couple of weeks at least.
Mr Karzai's decision was been warmly welcomed by world leaders.
US President Barack Obama described it as an important and constructive step forward.
"It is now vital that all elements of Afghan society continue to come together to advance democracy, peace and justice," he added.
US officials later said that the president had not yet determined whether to make a decision on sending more troops to Afghanistan before the runoff.
Sen Kerry said a second round of voting was a great opportunity and a turning point, praising Mr Karzai for the "genuine leadership in the decision he has made".
French President Nicolas Sarkozy said: "President Karzai's statement shows to all that he is a statesman who can decide on what is essential, in the higher interests of his country and of the unity of the Afghan people."
UK Prime Minister Gordon Brown also welcomed President Hamid Karzai's "statesmanlike" acceptance of the run-off.
Source: BBC
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