Zurich said in a press release Monday that the deal will see the Swiss firm become Australia's biggest life insurer with an approximate 19 percent share of the local market.
Both parties expect the transaction to be completed by the end of 2018.
Under the agreement, Zurich will have access to ANZ's estimated 6 million customers who are served through the bank's 680 branches, ATMs, and online services. That distribution deal is to be capped at 20 years.
In the statement, Zurich said the purchase is expected to contribute to the group's profitability "from day one."
Zurich said the deal will be financed through a mix of existing funds and senior debt.