The brisk pace of the US withdrawal comes as the Taliban insurgency ramps up its offensive throughout the country while peace talks in Qatar have failed to make significant progress.
The Pentagon said the turnover of Bagram airbase to Afghan security forces was a "key milestone" in the withdrawal.
Despite the rapid pace of the pullout, the US military currently still has the authority to protect Afghan forces.
"Those authorities still exist," Pentagon spokesman John Kirby told reporters, but did not give a timeline for when they might end.
US President Joe Biden said the withdrawal was on track, but some American forces would still be in Afghanistan in September as part of a "rational drawdown with allies."
Even so, the Bagram pullout brought an effective end to the longest war in US history.
The base, an hour's drive north of Kabul, was where the US military coordinated its air war and logistical support for its entire Afghan mission. The Taliban thanked them for leaving.
"We consider this withdrawal a positive step. Afghans can get closer to stability and peace with the full withdrawal of foreign forces," Taliban spokesman Zabihullah Mujahid said.
Other Afghans were more circumspect. "The Americans must leave Afghanistan and there should be peace in this country," said Kabul resident Javed Arman.
But he added: "We are in a difficult situation. Most people have fled their districts and some districts have fallen. Seven districts in Paktia province have fallen and are now under Taliban control."
For the international forces, more than 3500 of whom were killed in Afghanistan, the exit came with no pageantry. A Western diplomat in Kabul said Washington and its NATO allies had "won many battles, but have lost the Afghan war."
It was at Bagram, on a plain hemmed in by the snow-capped peaks of the Hindu Kush, that New York City firefighters and police buried a piece of the World Trade Center in December 2001, days after the Taliban were toppled for harbouring Osama bin Laden.
'BLACK SITE'
It was also here that the CIA ran a "black site" detention centre where terrorism suspects were subjected to abuse that then-President Barack Obama subsequently acknowledged as torture.
The base later swelled into a sprawling fortified city for a huge international military force, with fast food restaurants, gyms and a cafe serving something called "the mother of all coffees." Two runways perpetually roared. Presidents flew in and gave speeches; celebrities came and told jokes.
An Afghan official said the base would be officially handed over at a ceremony on Saturday.
US officials have told Reuters that the vast majority of troops have left Afghanistan, ahead of the timetable set by Biden, who had promised they would be home by September 11, the 20th anniversary of the attack that brought them to Afghanistan.
Biden said he thinks the government of Afghan President Ashraf Ghani, with whom he held talks at the White House last week, has the capacity to withstand recent Taliban advances. But he said Ghani's government should deal with "internal issues," an apparent reference to infighting among rival political factions.
'CONSEQUENCES'
Washington agreed to withdraw in a deal negotiated last year under Biden's predecessor, Donald Trump. Biden rejected advice from generals to hang on until a political agreement could be reached between the insurgents and Ghani's US-backed government.
Biden told Ghani in Washington last week the Afghans now must decide their own future. Ghani said his job was now to "manage the consequences" of the US withdrawal.
In exchange for the US withdrawal, the Taliban promised not to allow international terrorists to operate from Afghan soil. They committed to negotiate with the Afghan government, but talks in the Qatari capital Doha made little progress.
The US Embassy in Afghanistan this week said Washington was firmly committed to assisting Afghanistan and would provide security assistance of $3 billion in 2022.
The Taliban refuse to declare a ceasefire. Afghan soldiers have been surrendering or abandoning their posts. Militia groups that fought against the Taliban before the Americans arrived are taking up arms again.
A senior Western diplomat said the United States has asked three Central Asian nations - Kazakhstan, Tajikistan and Uzbekistan - to provide a temporary home to about 10,000 Afghans who worked with either US or allied forces.
Several European nations were also providing refuge to hundreds of Afghan employees and their families as they faced a direct threat from the Taliban.
Since Biden's announcement that he would press ahead with Trump's withdrawal plan, insurgents have advanced across Afghanistan, notably in the north, where for years after their ouster they had a minimal presence.
