Afghan government and Taliban sources have confirmed to Reuters that the militant group has now freed two professors, an American and Australian, that they kidnapped three years ago.
Kevin King and Timothy Weeks were taken from the American University in Afghanistan in August 2016.
The school in the capital has been the target of multiple militant attacks over the years.
The men are now said to be receiving care in the UAE.
Freedom for King and Weeks was uncertain until Tuesday's (November 19) confirmation.
Last week Afghanistan's President Ashraf Ghani said the Taliban had agreed to release the faculty in a prisoner swap for three senior Taliban commanders.
But then the swap was abruptly called off.
The decision to release the men is seen as a trust building exercise.
The Taliban usually refuse to negotiate with the Afghan government, and talk with the U.S. or Pakistan instead.
Two of the three Taliban commanders released are believed to be Hafiz Rashid and Anas Haqqani.
Haqqani is the younger brother of Sirajuddin Haqqani, the leader of the Haqqani Network, the most deadly faction inside the Afghan Taliban.
Earlier this year the Taliban said Anas Haqqani would be a member of any negotiating team that dealt with the United States, and demanded his freedom.