"They should be here on Tuesday or maybe Wednesday next week... we understand they just have to undergo a few medical tests before everything is cleared," said the woman's brother Dale van der Merwe.
Deborah Calitz and Bruno Pelizzari had been held hostage by Somali pirates for about 20 months before being released on Thursday.
Van der Merwe said the couple would fly to South Africa in a government aircraft and would probably land on a private airstrip.
Calitz's daughters had spoken to her after the announcement of their release.
"She said she was fine... a bit weak, but was happy to be coming home to see her girls and her grandchild which she hadn't met yet."
Van der Merwe said the families would allow the couple some time to relax and "take it all in" before celebrating.
"We plan on having several get togethers to welcome them back but also to thank everybody that was involved in our trying to get them back," he said.
He was not certain if their release had come after a ransom was paid.
The Associated Press reported that the couple seemed tired but happy to be going home.
"We are very happy to get our freedom again... we are so happy today [Thursday] and to join our families again," Calitz said at a news conference at the presidential palace in Mogadishu.
On Thursday, South Africa thanked the Italian and Somali authorities for the safe return of the couple.
Calitz and Pelizzari were kidnapped from a yacht off the south-eastern coast of Africa in October 2010.