National youth coach Mashaba was not present at the announcement in Soweto as he is in Mali with the under-20 squad.
“I am thrilled to be given this opportunity and will not disappoint the people of South Africa,” he replied when informed by telephone of his appointment.
South African Football Association (SAFA) president Danny Jordaan urged the public and media to be patient during a media conference.
“We ask for patience from the public and media — let us watch ‘Shakes’ grow into this job.
“His appointment was a unanimous decision by the national executive committee.
The humble 63-year-old former Orlando Pirates defender is a former caretaker coach and permanent coach of Bafana Bafana (The Boys).
He briefly took the reins in 1992 after the initial post-apartheid coach Stanley ‘Screamer’ Tshabalala was fired for hitting a journalist.
Mashaba assumed permanent control in 2002 only to be fired after a row with officials despite plotting a win over Ivory Coast that qualified the team for the 2004 Africa Cup of Nations.
Mashaba was the choice of the executive committee ahead of Portuguese Carlos Queiroz, who was favoured to take over the struggling national team.
Wage demands may have been a stumbling block with Queiroz, who has reportedly been offered $2.5 million (1.9 million euros) to continue coaching Iran.
Nigerian Stephen Keshi, whose contract was not renewed despite taking his country to the second round of the World Cup in Brazil, was another contender.
South Africa are ranked 14 in Africa and 66 in the world and poor tournament results cost Igesund his job.
Hosts South Africa were eliminated in the 2013 Africa Cup of Nations quarter-finals after losing a penalty shootout against Mali.
They also failed to qualify for the 2014 World Cup, surprisingly finishing second behind lowest seeds Ethiopia in a mini-league.
The first task for Mashaba will be to qualify for the 2015 Cup of Nations in Morocco by achieving a top-two finish in a group including Nigeria, Sudan and Congo Brazzaville or Rwanda.
Bafana Bafana have never beaten Nigeria in a competitive match and often struggled in the past against the combative Congolese.
South Africa face Sudan (away) and Nigeria (home) in September, Congo or Rwanda away and home in October and Sudan (home) and Nigeria (away) in November.