The vote has been put back at the request of the Bougainville Referendum Commission which had asked for more time to ensure the electoral rolls were as up to date as possible, Radio New Zealand International reported.
The new date for the writs is the September 27.
The Post Courier newspaper reported that the Prime Minister James Marape and acting Bougainville President Raymond Masono jointly announced the change in Port Moresby at the weekend.
Both governments said this would be the final deferment after an earlier deferral from June.
The leaders have called for Bougainvilleans to make use of the vote and ensure they are enrolled.
Meanwhile, the Bougainville Referendum Commission has invited applications from local and national groups to observe the conduct of the referendum.
Chief referendum officer Mauricio Claudio said observer groups would provide a critical role in the democratic process, by observing whether the conduct of polling and counting is free and fair, according to international standards.
"We encourage the participation of local, national and international groups in the referendum, to observe the process, and provide their independent report of polling and counting so that the referendum process is seen as a credible one by all involved," Claudio said.