The acquisition by Kina cost K24.2 million.
ANZ says the decision is in line with ANZ's simplification strategy, while also supporting customers with trade and capital flows in the region.
Kina Bank is a wholly-owned subsidiary of Kina Securities, a PNG company listed on the Australian and Port Moresby securities exchanges.
Kina's Greg Pawson said the acquisition was a great development for the group and for Kina Bank.
"Completing this acquisition represents a key component of our refreshed five-year strategic plan. The strength and capabilities that the acquisition will enable will allow us to better deliver on our purpose of empowering our customers and communities to have financial independence and security.
"The customers of ANZ PNG's business will benefit from this transaction. On day one there will be no change to their offering. Over the near future, their offering is expected to be enhanced as Kina continues to execute on its digital strategy. They will also experience Kina's differentiated value for money proposition," said Pawson.
ANZ said it remained committed to running a world-class institutional and large corporate banking business in PNG where it saw great opportunities for growth.
"ANZ has been in this market uninterrupted for more than a century and we continue to have a positive outlook for the PNG economy," ANZ's Graham Turley said.
"Our retail, commercial and SME operations in PNG are strong, successful businesses that will benefit from Kina Bank's focus on retail banking. ANZ will continue to service multinational corporations and large corporates operating in PNG," Turley said.
The sale includes all 15 ANZ branches with ongoing roles for all relevant staff in PNG.
The businesses being sold serve 85,000 retail and 6000 commercial and SME customers, and includes about $A150 million in lending assets and about $A450 million in deposits. The sale is not material to ANZ.
Subject to regulatory approval, the sale transfer is expected to be complete by late 2019.
ANZ will also continue to support economic growth and sustainable development in PNG through its financial literacy program MoneyMinded, which has trained more than 12,000 people since 2010.
ANZ has previously announced the sales of its retail and wealth businesses in Singapore, Hong Kong, China, Taiwan, lndonesia and Vietnam.
Its institutional bank has a presence in 15 markets in Asia and was ranked as a top four corporate bank in the region by Greenwich Associates in 2017.