The company will now establish a commission to look at making payments to Dutch Holocaust survivors and the family members of those who died.
It was a victory for Salo Muller, whose parents were sent by train to Westerbork in the eastern Netherlands when he was only five years old. They were later murdered in an Auschwitz gas chamber.
“What this means for me is that the NS sees that the suffering is not over; that very many Jews are still suffering,” Mr Muller told Dutch television.
“That is why I am so happy that they now see, on moral grounds … that reparations will be paid.”
The move comes four years after French rail operator SNCF agreed to pay £40 million for its role in moving around 76,000 Jews to the wartime camps.