Bryce Barker, who now lives in Australia, was held alongside fellow members of his research team.
They were doing fieldwork in a remote part of PNG's highlands when they were taken by a criminal gang from Hela Province who demanded a ransom for their freedom.
Their release brings to an end days of negotiations, and a complex security operation involving PNG police and defence personnel, in consultation with the Australian and New Zealand governments.
It comes two days after another woman who had also been taken was set free.
Foreign Minister Nanaia Mahuta praised the release on Twitter, welcoming their safe return.
Announcing the hostages' release on Facebook, PNG Prime Minister James Marape thanked police and defence forces, local leaders and the community for their assistance.
"We apologise to the families of those taken as hostages for ransom, it took us a while but the last three has been successfully returned through covert operations," he wrote.
"To criminals, there is no profit in crime. We thank God that life was protected."
The ABC reported that on 12 February, Barker shared a picture of his arrival in PNG's capital on social media, captioning it simply "Port Moresby".
His friend Cathy Alex, a highly regarded local program coordinator, replied: "Welcome to PNG".
The two would soon be reuniting and heading into the country's highlands as part of an ongoing archaeological research program with the University of Southern Queensland (USQ).
In a statement released to the ABC, USQ vice-chancellor Geraldine Mackenzie said the university was relieved to hear their much-loved colleague and his research team had been released.
"Professor Barker and his research team were in Papua New Guinea undertaking archaeological research," Ms Mackenzie said.
"Bryce is a highly regarded archaeologist and a valued colleague at the University of Southern Queensland and in the wider archaeological community. He has many years experience in undertaking research in PNG.
"Our deepest thanks go to the governments of Papua New Guinea, Australia and New Zealand, and the many people who worked tirelessly during this extremely difficult and sensitive time to secure their release."
Another New Zealander, pilot Phillip Mehrtens, is still apparently in captivity with separatist rebels after he landed a plane in Papua's remote highlands.
There is no new information about whether or not he will be released.