As of July this year, there were 124 asylum seekers in PNG.
From January, PNG will have responsibility for those who remain, the Australian and PNG governments said in a joint statement.
This means any asylum seekers still in PNG will be offered a pathway to permanent migration, including citizenship.
PNG will also provide support to those temporarily in the country awaiting transfer to a third country.
Prior to the December deadline, Australia will offer asylum seekers in PNG "voluntary transfer" to its offshore processing centre on the Pacific island of Nauru.
"This government's strong border protection policies - including a commitment to regional processing - have not changed," Home Affairs Minister Karen Andrews said.
"Anyone who attempts to enter Australia illegally by boat will be returned, or sent to Nauru."
Ms Andrews said PNG and Nauru had been longstanding partners in the fight against people smuggling.
"I thank them for their close cooperation and support," she said.
The federal government in September signed a new agreement with Nauru, which began offshore processing in 2012, to continue that arrangement.
There are about 107 detainees in Nauru.
Between 2008 and 2013, more than 50,000 people arrived in Australia on more than 820 boats and at least 1,200 died at sea, the government said.