Taliban officials said the hostages were freed at a "gesture of goodwill" because they were both seriously ill.
At the emotional handover they were able to walk to a Red Cross vehicle and afterwards South Korean officials said they appeared to be in good health. 'Heavy heart'
Kim Ji-Ung, a brother of Kim Gin-A, said he was relieved but "at the same time I have a heavy heart because of the other hostages who are still in captivity."
The Taliban kidnapped 23 members of a Christain aid group from their bus as they were travelling from Kabul to the southern city of Kandahar on July 19.
Nineteen South Koreans still remain in captivity. Two men from the group were shot dead after deadlines set by the captors for the release of Taliban hostages passed.
Roh Moo-Hyun, the South Korean president, told a cabinet meeting that he hoped Monday's releases "will be a good signal for the release of all the hostages".
"The government has to make greater efforts to have them released. We shouldn't relax until the last moment," he said.
Dan Nolan, Al Jazeera's correspondent in Kabul, said that both the Taliban and South Korean negotiators wanted to hold further face-to-face meetings after the apparent success of talks on Friday and Saturday.
"The South Korean delegation is waiting for a call from the Taliban to arrange another round of meetings. We understand that the Taliban negotiators involved in the previous talks are in the Ghazni area, so it appears both sides are keen," he said. German hostage
Meanwhile, there was concern for a man who identified himself as a German national abducted a day before the South Koreans. He told the AFP news agency in a telephone call on Monday that his captors wanted to kill him.
The man, who gave his name as Rudolph Blechschmidt, said that he was ill and appealed to the German government to help secure his freedom.
"I live with Taliban in the mountains," he said in an interview arranged by his captors. "I am in danger also, and I am very sick."
It has not however been possible to independently confirm the man's identity. Blechschmidt, a 62-year-old engineer, was captured on July 18 with a German colleague in the province of Wardak, near to Kabul.
His colleague, a fellow engineer, suffered circulatory failure a few days later and was then shot dead by the Taliban.
Four Afghans captured with the engineers are also believed to be held by the Taliban, who have demanded a release of prisoners in exchange for his life.
Source: Al Jazeera and agencies