Crime Branch joint police commissioner Ranjit Narayan led two and a half hours of questioning of Gibbs who he said was "part of the conspiracy" to fix match results for money during a tour of India in 2000.
"Gibbs was asked about his role in the entire episode and the illegal gratification offered to him to underperform or throw away matches," Narayan said in a statement on Thursday.
"In light of the information given by Gibbs today, further investigation to collect corrobative evidence shall be conducted.
"Gibbs has been informed that he may be questioned again should the need arise. He was cooperative and has agreed to provide any further information which may be sought later by the investigating agency.
"Gibbs admitted he was made the offer twice, first in 1996 and then in 2000. And he has revealed three names and we will be sending a letter rogatory (to South Africa) to seek their presence to question them in India."
Narayan noted that India had sent a first letter rogatory to South Africa in 2000 to which no reply has been received. "Gibbs lawyers described that as a huge mistake," the police chief said.
The 32-year-old South African, wearing dark glasses, was whisked away from the headquarters without speaking to the press.
"He is cooperating with us. He has given us a lot of leads," Narayan said.
None of the South Africa's current Test squad in India for the Champions Trophy were implicated, he added.
"We have certain information that helps us move forward."
Gibbs has admitted accepting money from disgraced former captain Hansie Cronje to score fewer than 20 runs against India in a one-dayer during a 2000 March-April tour.
He subsequently scored 74 runs and said he had "forgotten" about the deal, but was suspended and fined by the South African authorities.
Narayan said the whole South African team had received a match-fixing offer in 1996 but had turned it down.
India was also shaken by a betting scandal that rocked the national team in the late 1990s, but Narayan said Gibbs did not name any Indians.
Gibbs, who has played 79 Tests, has refused to tour India since 2000 after failing to obtain assurances he would not be detained.
Implicated in the same scandal was Cronje, who admitted involvement and was served with a life ban before dying in a plane crash in 2002.
South Africa, winners of the maiden Champions Trophy in 1998 in Bangladesh, are scheduled to play their first match against New Zealand in Mumbai on Monday.
The International Cricket Council in May said it would do everything possible to ensure Gibbs could tour India without fear of arrest.