The 20 have been identified as especially vulnerable out of the group of 280 mostly Afghan illegal immigrants detained on the tiny island.
New Zealand is to take nine adults, including six Iraqi women, and 11 children.
However, the New Zealand authorities insisted this was not a response to the recent high-profile hunger strike by some members of the group.
The refugees have been detained by Australia for more than two years after being rescued by the Norwegian freighter Tampa.
Immigration Minister Lianne Dalziel said on Tuesday the decision to take the 20 refugees, including six Iraqi women, followed a request from the UN High Commissioner for Refugees (UNHCR) for assistance, and preceded the hunger strike.
"The UNHCR considered this group to be particularly vulnerable and in need of permanent protection. None had been involved in the hunger strike," Dalziel said.
The hunger strike, which ended earlier this month, was staged in protest against continued detention.
"The UNHCR considered this group to be particularly vulnerable and in need of permanent protection. None had been involved in the hunger strike"
Prime Minister Helen Clark told radio Newstalk ZB New Zealand had been working with the UNHCR and the International Organisation of Migration, which looked after the people on Nauru.
She said the plight of the refugees was very miserable.
"We are taking 20 in response to UNHCR requests at this point and, as we have indicated in the past, if they come through with requests which we think hold water, we will look at them very seriously," Clark said.
Dalziel said the UNHCR and the Australian government were reassessing claims of some of the Afghan asylum seekers remaining on Nauru.
"If some of these are subsequently found to be refugees, it is possible New Zealand may be asked to accept further cases," she said.
"This would be a different situation to the humanitarian cases we have just accepted. However, we would consider such a request on its merits if it might further help resolve the situation on Nauru."