The Brazilian brought his 16-month reign to an end at a press conference after making the decision to return home to be with his ailing wife.
But Safa have said they will use him as a technical advisor in a consultancy role and Parreira has promised to help the national body select his successor, set to be named on May 6.
His current assistants, Pitso Mosimane and countryman Jairo Leal, have been placed in charge in the interim, with Safa silent on a long-term successor.
But the now ex-coach believes he has succeeded in his mandate to identify the top talent in South Africa and was keen to offer his services as a consultant in the future.
“I’m leaving, but if ever an opportunity avails itself where I can become involved on a consultancy basis, then I will offer my services,” Parreira said. “But the difficult job has been done – which was identifying players for World Cup. We have three players in every position and they can take it from there.”
“It was a very difficult decision to make but I need to dedicate more time to my family. I will remain available to ensure a smooth transition until the new coach is available.
“I regret very much that it has come to this but my family needs me, especially my wife. Every human being needs to find balance between their personal and professional lives.”
Meanwhile, Fifa has been made aware of Parreira's decision to resign.
"We would like to wish his wife a speedy recovery and hope that his presence will be of comfort and support on her road to recovery," a statement from president Sepp Blatter says.
“Safa now has the responsibility, with the help of Parreira, to find a new coach to ensure the continuation of the preparations of the South African national team for the Fifa Confederations Cup and the Fifa World Cup.
"The recent performance of Bafana Bafana shows that the team is moving in the right direction and we hope that this will be a positive movement towards 2010. We look forward to a wonderful time in South Africa and watching a successful team.”
