The decision was taken at an executive meeting of the FIFA ticketing committee in Zurich this week.
At the moment, tickets can be bought by filling in application forms at First National Bank (FNB) branches or fans can apply for tickets online.
The process has elicited an outcry from football fans who complained that it was too complicated to secure tickets for Africa's first world cup tournament.
"We are happy now to say that ordinary South Africans will be able to get the tickets," Jordaan said during a media briefing.
Jordaan said indications in the last two weeks have been that there is a positive feedback from South Africans to buy the tickets.
"We are particularly happy with the support behind Bafana Bafana and the pick up in ticket sales over the past two weeks," he said.
The South African Football Supporters Association (SAFSA) announced on Wednesday that the number of South Africans buying world cup tickets has increased by 24 percent.
South Africa was reported to have accounted for 79 percent of the total of applications received in the third phase of the ticket sales - 958,381 of the 1,206,865 applications received.
FIFA has also decided to increase the number of category four tickets available for South Africans. Close to two million tickets have been sold so far with six matches oversubscribed.
US and UK are still topping the sales followed Australia, Mexico, Germany and Brazil respectively.
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