He said the attacks, which were co-ordinated from Afghanistan, “cannot explain” why American forces should still be there 20 years later.
The US cannot continue to pour resources into an intractable war and expect different results, Mr Biden said.
The drawdown would begin rather than conclude by May 1, which has been the deadline for full withdrawal under a peace agreement the Trump administration reached with the Taliban last year.
“It is time to end America’s longest war,” Mr Biden said, but he added that the US will “not conduct a hasty rush to the exit”.
“We cannot continue the cycle of extending or expanding our military presence in Afghanistan hoping to create the ideal conditions for our withdrawal, expecting a different result,” Mr Biden said.
“I am now the fourth United States president to preside over an American troop presence in Afghanistan. Two Republicans. Two Democrats. I will not pass this responsibility to a fifth.”
The decision marks perhaps the most significant foreign policy decision for Mr Biden in the early going of his presidency.
He has long been sceptical about the US presence in Afghanistan. As Barack Obama’s vice president, Mr Biden was a lonely voice in the administration who advised the 44th president to tilt towards a smaller counterterrorism role in the country while military advisers were urging a troop build-up to counter Taliban gains.
Mr Biden has also made clear he wants to recalibrate US foreign policy to face bigger challenges posed by China and Russia.
Withdrawing all US troops comes with clear risks. It could boost the Taliban’s effort to claw back power and undo gains toward democracy and women’s rights made over the past two decades .It also opens Mr Biden to criticism, mostly Republicans and some Democrats, even though former president Donald Trump had also wanted a full withdrawal.
The statement was followed by confirmation from Defence Secretary Ben Wallace of the “drawdown” of UK troops as well.
He said: “The people of Afghanistan deserve a peaceful and stable future.
“As we drawdown, the security of our people currently serving in Afghanistan remains our priority and we have been clear that attacks on Allied troops will be met with a forceful response.
“The British public and our Armed Forces community, both serving and veterans, will have lasting memories of our time in Afghanistan.
“Most importantly we must remember those who paid the ultimate sacrifice, who will never be forgotten.”
A former defence minister warned the US decision to withdraw its troops risks “losing the peace”.
Senior Conservative MP Tobias Ellwood said the subsequent vacuum could allow extremism to “regroup”.
Speaking to Times Radio, Mr Ellwood said the president’s foreign policy decision was “concerning” and “not the right move”.
“It reflects the troubles we’ve had in interventions over the last couple of decades where we win the war, but lose the peace,” the chairman of the Commons Defence Committee said.
“We don’t put enough effort into the stabilisation and the peacekeeping, the nation building, and encouraging better governance, better security, that indigenous capability so they can look after their own affairs.
“Instead, as we’ve seen in Iraq as well, we defeat the bad guys and then we withdraw, we don’t do enough to then lift the country off its knees.
“And I fear that we will see – in fact it’s happening already – is extremism will regroup in Afghanistan in the way that it’s regrouping in Iraq, and indeed, to some degree in east Africa as well.”