The centre was originally built as a World War II military barracks, and agencies are all in different buildings.
"All the services will now be under one roof, [making] it much more convenient and efficient," Mr Bah said.
"It is also fantastic that people who are fleeing war are not being welcomed into their new country at a military barracks."
About 30,000 people had stayed at the centre since it started operations in 1979, and the new buildings would be able to support a sudden intake at short notice.
This month, the Government announced that the annual refugee quota would be increased from 750 to 1000, effective from 2018.
The quota has remained at 750 refugees a year since it was introduced in 1976.
Minister for Ethnic Communities Peseta Sam Lotu-Iiga said the centre helped prepare refugees for life in New Zealand.
"They finally have a place here in New Zealand that they can call home, a place they feel safe," he said.
Refurbishment had taken place in stages, and the new design included a soccer field and more open green space.
"Up to 220 refugees can be housed at the centre. There is enough space to kick a ball around, enjoy family time, make new friends or simply enjoy some quiet time in reflection," said Mr Lotu-Iiga.
The centre's opening comes ahead of World Refugee Day on Monday, which will be marked with events in Parliament and around the country.
Red Cross, the primary provider of community refugee resettlement here, is calling for Kiwis to "stand in each other's shoes" to mark the day.
The campaign aimed to help New Zealanders meet and learn about people of different cultures who now call New Zealand home.
AUT Centre for Migrant and Refugee Research director Max Abbott said the current global refugee crisis was unprecedented, and more needed to be done to lift New Zealand's contribution.