In a video released yesterday through its media wing, the group said it had consulted religious leaders and they had advised "that we should release these prisoners".
Al-Nusra had originally demanded various terms for the release of the peacekeepers, including the delivery of aid to areas besieged by the Syrian government, the release of prisoners and the group's removal from a UN terror blacklist.
A Fijian peacekeeper, who did not identify himself, also spoke in the footage, confirming that the group had pledged to free the soldiers.
"We have been informed that we will be released soon and we are all very happy to be going home."
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The peacekeeper adds that the troops "are all safe and alive" and thanks Al-Nusra "for keeping us safe and keeping us alive."
"I would like to assure you that we have not been harmed in any way," he says.
The peacekeepers, all Fijian nationals, were taken hostage two weeks ago when Al-Nusra fighters stormed the Syrian side of the Quneitra crossing that leads to the Israeli-occupied Golan Heights.
On Wednesday, a Fijian government spokesman told AFP that the posts were the result of someone having "misinterpreted" the situation.
The Fijians are part of the UN Disengagement Observer Force (UNDOF), which has been stationed in the Golan Heights since 1974 to monitor a ceasefire between Israel and Syria.
There are currently 1,200 peacekeepers from the Philippines, Fiji, India, Ireland, Nepal and the Netherlands.