IAG, which owns the NZI and State (NZ) brands, was the country's largest insurer before the deal.
AMI is currently the second-largest insurer.
Big staff changes are not planned at AMI, whose chief executive is John Balmforth.
"We are not saying he will leave," Jacki Johnson said. "We are having very short conversations and we are working through the integration and then there's a lot of decisions that have to take place after integration.
"We have a whole set of things that we have to sort out, given the size of IAG and the roles and responsibilities. I've had very good discussions with John overnight. We have been working closely with John who says he will stay on and help through the integration."
IAG is buying a new company which owns all the AMI business except the Canterbury earthquake claims, which will remain with the current company, to be owned and backed by the Government and given a new name.
AMI has been seeking capital since the Government announced a $500 million financial backstop that allowed the insurer to cope with rising reinsurance costs and Christchurch earthquake claims of nearly $2 billion.
AMI chairman Kerry Nolan said the IAG deal and the Government's agreement to back a separate earthquake claims resolution business was the best possible outcome for policy holders, earthquake claimants and other stakeholders.
Finance Minister Bill English said the deal looked "pretty reasonable" but the numbers would depend on how much the Christchurch claims would cost the Government.
"If the claims turn out to be bigger than expected the deal will cost us a bit more," he said. "If they turn out to be about where we expect, the deal might cost us nothing."
The alternative to accepting the deal would have been the Government effectively owning the insurance business of AMI.
He said the Government had to manage the Christchurch claims because no business had been interested in those "but we didn't want to be running one of New Zealand's larger insurance businesses".
The net liability at this stage looked to be $120 million and provision for $300 million had been factored into Government books.
The deal
* IAG will buy AMI for $380m.
*IAG will keep the AMI name.
*AMI's liabilities for earthquake claims will be taken over by the Government.
*The deal is subject to regulatory approval.