The match-fixing scandal involving the South African national team is to be investigated by an independent enquiry backed by Fifa.
"This long-standing open case is harming South African football," said Fifa secretary general Jerome Valcke.
"It is vital this matter is concluded soon, with the culprits sanctioned under the zero tolerance policy."
Fifa found the 2010 World Cup warm-ups against Bulgaria, Thailand, Colombia and Guatemala had been fixed.
Nematandani was present at Friday's meeting between Valcke and South Africa Sports Minister Fikile Mbalula.
Fifa said the mandate of the judicial committee "will be limited to matters related to the case of irregularities related to friendly matches of the Safa in the build-up to the 2010 World Cup."
Michael Garcia, head of the judiciary arm of Fifa's ethics committee, could also join the commission, subject to constitutional approval.
"It is critical that structures are set-up in order to tackle similar cases should they happen in the future," added Valcke.
"I am very pleased by the commitment of the South African government and also Safa to make sure this matter is now dealt with as a highest priority.
"Fifa will provide any advice and support possible both at investigatory and disciplinary level. To this effect a representative from Fifa's Security Division was also at today's meeting."
Allegations of match-fixing were first revealed in the South African press in July 2011 but Safa did not immediately act.
The issue was only raised once Fifa had incorporated the country into a wider investigation into Wilson Raj Perumal, a Singaporean jailed for two years for masterminding a match-fixing scheme in Finland.
Nematandani and four other top officials were briefly suspended following the handing over in December by Fifa to Safa of a 500-page investigation into the activities of Perumal and his Football 4U organisation.
But within a month their suspension was lifted on procedural grounds.