"There were many great candidates that I considered but I am delighted that Tommy has accepted this position," Igesund said in a statement.
"I look forward to working with him with immediate effect."
South African Football Association (Safa) chief executive Robin Petersen thanked Supersport for releasing Madigage at short notice for national duty.
"We are grateful to the club for allowing us to take Tommy into our national team structures," Petersen said.
"We realise this has a negative impact on them, but we applaud them for allowing us to put the country first."
'Input and support'
Serame Letsoaka was appointed as second assistant coach for the national team's training camps, and Alex Heredia was named goalkeeper coach.
Fanyana Sibanyoni, the chairperson of Safa's technical committee, said Igesund had requested that a reference group be put in place to provide "input and support".
The reference group would consist of Shakes Mashaba, who had been in line for the head coach's job, Clive Barker and Jomo Sono.
"We are delighted with this 'brains trust'," Sibanyoni said.
"They will assist the coach as needed by him. Gordon recommended this panel to us, and we are convinced that this panel will provide him with the necessary support he needs in getting the best out of the team." – Sapa