The house was debating a Senate recommendation the Government accept the offer.
New Zealand has, for several years, offered to take up to 150 of the refugees - an offer Canberra has always spurned, citing concerns the refugees would have easy access to Australia.
Daniel Webb from the Human Rights Law Centre said the House got it right on Monday.
He says after four-and-a-half years filled with fear, violence and limbo it was time for the Australian government to evacuate these men to safety, not obstruct viable ways forward and leave them indefinitely languishing in danger.
Hundreds of refugees remain on Manus Island and are now being held in unsecured and incomplete facilities close to the main town.
The UNHCR has said these facilities are "severely inadequate".