The exchange for one American and one Australian imprisoned by the militant group was announced by the Afghan government on November 12 but was delayed when the commanders did not land in Qatar earlier.
The Taliban released two Western hostages in southern Afghanistan Tuesday, handing them over to US forces more than three years after they were abducted in Kabul, insurgent sources and police told AFP.
The release of American Kevin King and Australian Timothy Weeks, both professors at the American University in Kabul, comes one week after President Ashraf Ghani announced that Afghanistan would free three high-ranking Taliban prisoners in an apparent swap that he hoped would help jumpstart peace talks.
"This morning at around 10:00 am two American University professors were released in Nawbahar district of Zabul province. They were flown out of Zabul by American helicopters," a local police source said.
Three Taliban sources in the province also said the hostages had been released.
"We released the professors and are now expecting the Kabul government and Americans to release our three prisoners as soon as possible," one of them told AFP.
There was no immediate comment from the US embassy in Afghanistan. Afghan officials in Kabul said they would release a statement shortly.
The three Taliban commanders had earlier landed in Qatar.
The Afghan government's decision to carry out the swap is seen as key to securing direct talks with the militants, who have, until now, refused to engage with what they call an illegitimate "puppet" regime in Kabul.
"Our three prisoners had been freed on Monday night," said one of the sources, a senior Taliban leader in Afghanistan, who declined to be identified because he was not authorised to speak publicly about the deal.
"Soon after their release, they were flown to Doha and handed over to the political office in Qatar."
Representatives of the Afghan government and the US embassy in Kabul were not immediately available for comment.
On November 12, President Ashraf Ghani said Afghanistan would free Anas Haqqani, a senior figure in the eponymous Haqqani network responsible for some of the worst violence in recent years, and two Taliban commanders.
But the swap was abruptly postponed, with the Taliban shifting their hostages to a new location after the commanders failed to land in Qatar.