"We received with sadness the news that Pierre (Korkie) was killed in an attempt by American Special Forces, in the early hours of this morning, to free hostages in Yemen," said the Gift of the Givers group, which has been negotiating his release.
"The psychological and emotional devastation to (his wife) Yolande and her family will be compounded by the knowledge that Pierre was to be released by Al Qaeda tomorrow," it said.
The couple from the central South African city of Bloemfontein had worked as teachers in Yemen for four years.
Yolande was released in January following mediation by Gift of the Givers, which said Pierre's release was just hours away when the US launched an operation to free the hostages, who included US captive Luke Somers.
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"A team of Abyan leaders met in Aden this morning and were preparing the final security and logistical arrangements, related to hostage release mechanisms, to bring Pierre to safety and freedom," the charity said.
"It is even more tragic that the words we used in a conversation with Yolande at 5.59 this morning was 'the wait is almost over.'
"Three days ago we told her "Pierre will be home for Christmas". We certainly did not mean it in the manner it has unfolded."
US Defense Secretary Chuck Hagel said that the hostages' captors murdered them during the raid.