FIFA will pay for the building called SAFA House which is due to be completed by next July and will serve as headquarters of the 2010 World Cup organizing committee and the temporary home of FIFA during the tournament.
FNB stadium will be one of the main venues for the World Cup finals.
"It is time to build this house upon which foundation lies trust and confidence from FIFA that South Africa will host a good World Cup in 2010 Blatter said according to the South African Press Association.
Last year South Africa won the right to become the first African country to hold the World Cup finals.
Organizers hope to keep construction costs to a minimum by refurbishing existing venues and only building new stadiums in areas where there is a need for a sporting complex which will be used after the event.
South African authorities say they are confident the country will cope with the influx of tourists during the event but there are real concerns about the lack of good quality public transport for visiting fans.
South Africa failed to qualify for next year's finals in Germany. Coach Stuart Baxter resigned last week after long-standing complaints that SAFA officials were preventing him from doing his job. A new coach has to be named.