Worth $A125 million, the acquisition is subject to both parties gaining the necessary statutory, regulatory and third party approvals. The deal is expected to be completed by the middle of next year.
The move is part of BSP's plans for regional expansion, and position itself as the Pacific's leading financial services provider.
Westpac will continue to own and operate its branches while the while the deal is being concluded.
Bank of South Pacific CEO Robin Fleming said: "BSP chairman and executive will undertake a program of pre-completion visits over the next few months to introduce customers and staff in those pacific island countries and make initial support representations to local regulatory authorities, emphasising that there will be a smooth transition post completion."
Chairman Kostas Constantinou said BSP was committed to the region and looked forward to developing the economies of the Pacific and Papua New Guinea.
"It is a regional strategy (and) we have and will continue to have a strong presence in the region for a very long time. BSP is living up to its name as the Bank of South Pacific," he said.
Based in PNG, the Bank has assets of about K16 billion and has developed a strategic interest to find opportunities, build commercial relationships, and grow its presence in the region.