Igesund, the 17th coach in 20 years for South Africa, replaces Pitso Mosimane, who was sacked this month after a poor start to the 2014 World Cup qualifiers.
He has been offered a two-year contract after a meeting with officials in Johannesburg on Saturday.
The 55-year-old Igesund has been the most successful coach in South African league football over the past 15 years, winning four league titles with four different clubs. He almost won a fifth in May with another club, Moroka Swallows, but they finished runners-up.
Igesund has been coaching in South Africa since 1986, and before that had a successful playing career as a striker in the South African league and a spell in the Austrian league.
He will take charge of South Africa for the first time in a friendly against Brazil in Sao Paulo on September 7.