Biswajit Guha, assistant director of zoology at the Singapore Zoo said the noise of the attack caught the attention of nearby keepers and they eventually managed to distract the tigers and rescue Nordin.
Zoo vets fought to save the man but he died soon afterwards.
Mr Guha said: "Keepers managed to separate the worker from the tiger. While waiting for the ambulance, our vets attended to him.
"The worker tragically succumbed to his wound."
Local media reports said Nordin was seen behaving in an agitated manner before he leapt into the moat.
Mr Guha said the cleaner worked at the chimpanzee area and was on his lunch break when the tragedy happened.
"They saw him riding off on a bicycle and coming back in through the front entrance again, and then about five minutes later, the whole alert came on the walkie talkie," he said.
The man is said to have told colleagues: "Goodbye, I won't be seeing you again".
Staff were able to reach the him only once the tigers returned to their dens, leaving him in the passageway.
Visitors near the enclosure screamed and cried out for help as the watched the attack.
According to conservation group WWF, there are about 4,000 tigers left in the world and they are considered an endangered species.
White tigers are even rarer because they suffer from a genetic condition that strips their fur of the orange pigment, leaving the animal with snow white fur, black stripes and blue eyes.