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Mr Boochani, who is an award-winning author, journalist, and advocate for refugees held in a detention camp on Manus Island by the Australian government, flew into Auckland last night with a visitor visa.
At the airport, he told reporters this was the first time he had felt happy in a long time.
"I survived, you know, when I was in Manus or Port Moresby. I was just thinking about getting freedom ... affect Australia, challenge Australia, make people aware of this situation. But I think it's the first time that I feel happy because I survived."
The journalist has been detained on Manus Island since 2013 after arriving in Australian territory by boat.
He wrote the book No Friend but the Mountains on a smartphone app while imprisoned on the island, and won multiple international awards including Australia's richest literary prize.
This morning, he was welcomed in Christchurch, where he will be a special guest at a literary event on November 29, by Mayor Lianne Dalziel and Ngāi Tahu.
According to the Guardian, he took a 34-hour journey across three countries and six timezones in the Asia Pacific before reaching New Zealand.
He told RNZ's Morning Report programme today it was a long journey with struggles from PNG to New Zealand.
"It was quite hard to travel with a blue passport, which is for the UNHCR for the refugees, because at Port Moresby in the airport they ask many questions and it took a long time to get in the plane, in Philippines it was like that too, and in New Zealand.
"So I think it's natural everywhere that you travel with that [passport], people they don't treat you in the way they treat others, but it's fine. I'm tired but happy."
Asked whether he would want to apply for asylum in New Zealand, he said he did not want divert his attention away from the objective of his visit, which is sharing his story in the book.
"I prefer to be free of any protest for a while in the time here, because it's the first time I can walk as a free man, that's why I prefer not to talk about this anymore.
"I want to be here for a while, and later we will look at that possibility, because I'm already accepted by America so for now I prefer to focus on this story and share it with people."
Before leaving Port Moresby, Mr Boochani told the ABC he would never be going back, saying he wants to be somewhere where he is a person, not just a number.
Mr Boochani was recently accepted for resettlement in the United States and told ABC at Port Moresby that he was investigating whether he could fly from New Zealand to the US, once the process was completed.
"First, I would like to just spend some time as a free man, but after that I will look at that - is it possible that I go to the US from New Zealand? Or I should stay there?"
He told Morning Report he was happy to be a free man now and his new journey would involve understanding what freedom means, and enjoying the change of seasons for once.
"I told my friends and colleagues here that the first thing that's very interesting for me is I feel freedom, because I was in a tropical area for almost seven years ... so this is a very new thing for me ... so I think it will take time that I understand freedom and completely understand that I am a free man now."
Green MP and spokesperson for human rights Golriz Ghahraman, who travelled with Mr Boochani to Christchurch, told Morning Report she had not yet had a proper sit-down and chat about the journey with the journalist yet.
"It was another slightly harrowing journey [to New Zealand] from the sounds of it, but we received him on a flight coming from Manila."
Claiming asylum is a fundamental right that the country's laws recognise, and Mr Boochani has the right to do so, Ms Ghahraman said.
In a statement, Mr Boochani said he wanted the New Zealand Government to do more to help the hundreds of detainees who remain in PNG.
The Manus Island centre officially closed in 2017, but 250 of the 1500 detainees remain in Papua New Guinea.
New Zealand has repeatedly offered Australia to resettle 150 refugees a year from the offshore detention centres but has been rebuffed.
Ms Ghahraman said she was heartened by Prime Minister Jacinda Ardern's actions and that the offer remains on the table.
"The issue is also we actually need to keep our voice really loud on human rights issues, on refugee issues, as an independent voice on the world stage - as New Zealand has always been - so I think we really have a role to play there as well."
Human rights watchdog Amnesty International said in a statement it was sponsoring his month-long visitor visa and called on the Australian government to release the hundreds of people remaining in offshore detention.
Boochani has been a prominent critic of the treatment of people under Australia’s hardline immigration policy.
Asylum seekers intercepted at sea are sent for "processing" in PNG and on the South Pacific island of Nauru, where many have languished for years. They are permanently barred from settling in Australia.
- additional reporting by Reuters