The two were voted into powerful committees at the congress of world football's governing body in Mauritius at the weekend.
Mabaso-Koyana, who is the group financial officer of the Passenger Rail Agency of South Africa, is the deputy chairperson of Fifa's audit and compliance committee, which will essentially see to it that no money is being stolen.
It is an eight-member committee.
Hack, a prominent lawyer in Johannesburg and chairman of the Confederation of African Football's disciplinary structure, was voted to the disciplinary committee as one of the two African representatives.
The other is the Democratic Republic of Congo's football federation president Constant Omari Selemani.
It is a rare election win for South Africans.