Three South Korean women were released first, and later five -- four women and a man -- handed over to members of the International Committee of the Red Cross (ICRC) in Ghazni province, Reuters witnesses said.
Wearing long, traditional headscarves, the three women who were first to be freed wept as they sat in an ICRC vehicle.
Taliban representative Qari Mohammad Bashir, who was involved in the negotiations that led to the agreement to free the Koreans, told the Pakistan-based Afghan Islamic Press news agency he hoped all would be free in two or three days.
Earlier, South Korean Foreign Ministry spokesman Cho Hee-yong said the three women who were released first had been handed over to Korean custody and were apparently in normal health.
The insurgents seized 23 Korean Christian volunteers on July 19 from a bus in Ghazni province. Two male hostages were killed by their captors early on in the crisis.
The Taliban released two women as a gesture of goodwill during the first round of talks but said on Tuesday they had reached a deal on the release of remaining 19.
South Korea's presidential Blue House said the agreement was on condition it withdraw its troops from Afghanistan within the year and stopped its nationals doing missionary work in Afghanistan.
However, South Korea had already decided before the crisis to withdraw its contingent of about 200 engineers and medical staff from Afghanistan by the end of 2007. Since the hostages were taken it has banned its nationals from traveling there.
A spokesman for South Korea's president, Chon Ho-seon, did not respond to questions at a news briefing in Seoul on Wednesday on whether a ransom was part of the deal but said South Korea had done what was needed.
We believe it is any country's responsibility to respond with flexibility to save lives as long as you don't depart too far from the principles and practice of the international community, Chon said.
Two Indonesians were also involved in the negotiations, Indonesia said.
Relatives waiting in South Korea cheered when news of the releases came through, said a representative of the families.
We want to see all of them released, representative Lee Jeong-hun told reporters.
(With additional reporting by Sayed Salahuddin in KABUL, Jack Kim and Jessica Kim in SEOUL)