Mark Frerichs was working as a civil engineer on construction projects in Afghanistan when he was "taken hostage", Washington previously said, AFP reported.
"After long negotiations, US citizen Mark Frerichs was handed over to an American delegation and that delegation handed over (Bashar Noorzai) to us today at Kabul airport," Afghan acting Foreign Minister Amir Khan Muttaqi said at a press conference.
"We are happy that at Kabul International Airport, in the capital of Afghanistan, we witnessed the wonderful ceremony of one of our compatriots returning home."
Noorzai was welcomed with a hero's fanfare by the government of the newly styled Islamic Emirate of Afghanistan (IEA).
Photos show he was greeted by masked Taliban officials bearing floral garlands.
"If the IEA had not shown its strong determination, I would not have been here today," Noorzai told reporters at a press conference.
The Taliban seized power in Afghanistan a little over a year ago as the United States and their NATO allies withdrew from the country after 20 years of military intervention.
Since then, the nation has been further plunged into economic and humanitarian hardship, with billions in Afghan assets abroad frozen by Washington and international aid vastly reduced.
No country has yet to recognise the new government, with Washington repeatedly telling the Taliban that they will have to "earn" legitimacy.