The Qatar Airways charter flight landed in the Qatari capital Doha on Thursday, with a second flight due on Friday.
US Secretary of State Antony Blinken urged help with evacuations during a recent visit to Qatar.
Hundreds of Afghan citizens who had helped the US military were unable to get out in last month's US airlift.
Reuters news agency reports that 113 people were on board the plane.
UK Foreign Secretary Dominic Raab said 13 British citizens had arrived in Doha, and thanked Qatar for facilitating the flight.
Dutch foreign minister Sigrid Kaag has also tweeted her thanks to Qatar, saying that 13 Dutch nationals were on board.
And the White House released a statement confirming that US citizens had flown, and also thanked Qatar, saying the flight was the result of "careful and hard diplomacy and engagement".
The statement also said the Taliban had been "businesslike and professional" in helping the US citizens fly out.
In a press conference held at the airport, Qatari special envoy Mutlaq bin Majed Al Qahtani described Kabul international airport as operational and said it was a historic day for Afghanistan.
finished last month, following the Taliban takeover of the country on 15 August.
More than 124,000 foreigners and Afghans fearful of Taliban retribution were flown out of the country.
Around 100 US citizens were thought to be left in Afghanistan before the flight.
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