The Pacific nation has granted its first refugee visas since Nauru's immigration detention centre reopened in 2012.
Nine Iranians - including a mother, daughter and son - and four Pakistanis are the first people to have been released into the community.
Minister Morrison confirmed that 20 asylum seekers on Nauru have had their refugee determinations handed down, with 14 asylum seekers receiving positive assessments and 7 applicants receiving negative assessments.
A further 21 refugee claims are to be finalised today.
Mr Morrison says the refugees are receiving 5-year-visas which enable them to work, leave and re-enter the country, but they will not be able to come to Australia.
He says access to services and a living allowance isn't guaranteed.
"The services are provided on a needs-basis, not an entitlement basis when it comes to this support. It will take account of individuals' own resources they may have to support themselves where they are," he said.
"But the services include things like language training, vocational training, connecting people to employment, a general orientation. There is an initial six-week intensive resettlement arrangement. It is all designed to get people standing on their own feet within 12 months."
In a statement Nauru's Justice Minister says he's confident refugees will find peace and fulfilment in his country.
Meanwhile, the Australian Greens say Nauru is not ready to resettle refugees after the Pacific nation granted its first refugee visas since the immigration detention centre there reopened in 2012.
An Iranian mother, daughter and son, and a group of four single men are the first people to have been released into the community.
The Greens' immigration spokeswoman Sarah Hanson-Young says Nauru is not prepared to accommodate the refugees.
"It is a broken state. You know it takes 20 minutes to drive around the entire island, and there is decrepit housing, the hospital is falling apart, the local school was actually funded by Australian - AusAID money some years ago," she said.
"There are not the appropriate services for local Nauruans let alone the damaged refugee children that are about to walk out of that centre. It is an awful, awful circumstance that Mr Morrison is forcing these children into."
