NIB has taken on 120 staff who worked for Tower, whose headquarters are at 22 Fanshawe St where Fitzgibbon said it would remain "for the foreseeable future".
Tower holds about 13 per cent of the market, compared to Southern Cross's 65 per cent.
Dental insurance, the youth market and employer group schemes are just some of the areas where Fitzgibbon sees growth opportunities.
"I identified dental insurance in my early reconnaissance. That stands out in terms of cover in the market. About 55 per cent of Australians have a level of dental cover but in New Zealand it's very, very low. It's nothing like 55 per cent and it's one of those areas where families incur large out-of-pocket costs. A lot of what health insurers pay for is hospital costs but relatively few people end up in hospital. Yet just about everyone goes to the dentist," he said.
He also sees big opportunities to market insurance directly to consumers.
"The Tower business insurance policies are mainly sold through brokers. So it's important we maintain our relationship with the brokers and financial channels but the other main chanel is through employers. We see that as a growth corridor. The third one is direct to consumer but in Australia, 90 per cent is sold direct to consumers," he said.
That pointed to a big marketing drive to sell new policies.
"Southern Cross has been a very successful business. We don't see ourselves as eating into their share but rather want to see the market grow as a whole. Only 30 per cent of the New Zealand population is covered so there appears to be lots of opportunity but in Australia, 55 per cent of the population hold some form of health insurance," Fitzgibbon said.
The business is being renamed NIB NZED and is seeking a chief executive - who Fitzgibbon said would be a New Zealand resident - and a board chairman.
Tower Health did not have its own boss but was run as a division of the Tower group, he said.
Peter Tynan, Southern Cross Health Society chief executive, said NIB's arrival would not result in any changes for his members.
"While the entry of a new competitor is always of interest, it will not cause us to divert from our current focus," Tynan said, adding the society was focused on delivering value.
"Southern Cross is a very different business to NIB. We operate solely for the benefit of our members and our core focus is to return as much value as possible to them. We do not operate to make profits for overseas shareholders," Tynan said.
"We believe a strong private health insurance market is good for New Zealand."
Sizing up
Tower Health Insurance: 170,000 policy holders
Southern Cross Health Society: 822,422 members
NIB: now owns Tower Health
* Covering Australians for 60 years.
* 30 per cent of New Zealanders have health cover.
* 55 per cent of Australians have health cover.
Sources: NIB, Southern Cross