The IAG insurance group is offering to buy AMI for $NZ380 million.
AMI received a $500 million financial backstop package from the Government in April, after it admitted it might not have enough in reserves to pay insurance claims from February's quake in Christchurch.
Its board has now accepted a conditional offer from the IAG, to buy all of the company, except $1.8 billion worth of claims relating to the earthquake.
They will be held in a Government-owned company, which will be set up shortly. It will progress claims and fund a shortfall estimated at $300 million.
IAG already owns State Insurance and NZI in New Zealand. It plans to keep the AMI brand for its 500,000 customers.
The deal needs approval from the Reserve Bank, Commerce Commission and Overseas Investment Office. It is expected to become unconditional early next year.
Finance Minister Bill English says a takeover of AMI earthquake claims by the Government will provide certainty for homeowners.
Mr English says discussions began about AMI testing the market for a buyer and the resulting deal should benefit Christchurch residents.