The announcement comes after talks between South Korean diplomats and Taliban negotiators today.
A spokesman for the government in Seoul, Cheon Ho-seon, said the 19 would be released in return for the pullout of South Korean troops from Afghanistan within this year and a pledge to stop sending Christian missionaries to the country.
The militant group's representative, Qari Bashir, told RFE/RL's Radio Free Afghanistan that the Taliban have also demanded that South Korea withdraw all its aid workers from Afghanistan by the end of month.
Bashir said the Taliban have accepted that South Korea has no influence over the Afghan government's refusal to release imprisoned militants.
The captors initially demanded that the Afghan government free Taliban prisoners in exchange for the lives of the hostages.
Bashir said the Taliban have guaranteed the safety of all South Korean nationals -- including several hundred noncombat troops -- during their withdrawal from Afghanistan.
South Korea has some 200 medical and engineering troops in Afghanistan who are participating in UN-backed reconstruction efforts.
Bashir predicted that it would take three to four days until the hostages are released "because they are being held in different locations and need to be transferred to one place."
Militants abducted 23 South Koreans from a bus traveling between Kabul and Kandahar on July 19.
They killed two men among those hostages and later released two sick women.