The 63-year-old, who has also previously led Finland and the England Under-19 side, coached South Africa in 2004 and 2005 but was axed after the team failed to qualify or the 2006 World Cup in Germany.
He returned to South African football in 2012 as coach of local club side Kaizer Chiefs, which he steered to two domestic league championships in three years before leaving for a brief stint with Turkish top-flight team Genclerbirligi.
Baxter was appointed to lead South African club SuperSport United in Jan. 2016 and will remain with them until the end of the current campaign, before taking up his duties with the national association.
"SAFA believes that the coach has the necessary skills to navigate the tough qualification path for the African Nations Cup and the FIFA World Cup," South African Football Association CEO Dennis Mumble said in a statement.
SAFA first suspended and then sacked former coach Ephraim Mashaba in November last year after a public outburst aimed at the organisation’s president, Danny Jordaan, following a 2-1 World Cup qualifier victory over Senegal.
Mashaba was unhappy at what he saw as a lack of support from the SAFA hierarchy in the months leading up to the match.
South Africa’s next competitive fixture is on the weekend of June 9-11, when they start their 2019 African Nations Cup qualification campaign away in Nigeria.
(Reporting By Nick Said, editing by Larry King)
