Deputy Prime Minister Winston Peters is calling for the "depraved" mosque gunman to be extradited back to Australia to avoid this country having to pay to keep him locked up for life.
The sentence raises questions about whether he could ever conceivably be deported back to his native Australia.
Prime Minister Jacinda Ardern, who has not publicly uttered the gunman's name, said those were questions for another day as today was about the sentence.
But she added there was currently no legal basis for extradition, and if it were to happen, the wishes of the victims' families would be paramount.
However Peters said now was the time "for Australia's Minister of Home Affairs, Peter Dutton, to receive and carry out the terrorist's sentence in Australia".
"The Islamic community and all of New Zealand has already suffered enough without having to pay astronomical prison costs to keep him safe in our prison system."
Peters hoped the sentence with help to heal those affected.
"The judgment is the only one that matched the depravity of the terrorist's crimes against the Islamic community, and it's devastating effect on all people living in this country," he said.
"The Islamic community and all of New Zealand has already suffered enough without having to pay astronomical prison costs to keep him safe in our prison system."
Australian Prime Minister Scott Morrison said in a statement that justice had been delivered "to the terrorist and murderer for his cowardly and horrific crimes in Christchurch".
"It is right that we will never see or hear from him ever again," Morrison said.
"All Australians were horrified and devastated by his despicable act. New Zealand is family to us.
"Today, we send our love across 'the ditch' and I had the opportunity to pass on those wishes earlier today to New Zealand PM Jacinda Ardern."
Morrison said Ardern had not raised the issue of extradition with him.
"It's normal practice that criminals convicted of these offences serve their sentences in that jurisdiction, and that's my understanding of what the arrangements are and no request has been made to Australia for that to be any different."
Earlier, Ardern welcomed the life without parole meted out to the mosque gunman for his "horrific, despicable act".
"The trauma of March 15 is not easily healed, but today I hope is the last where we have any cause to hear or utter the name of the terrorist behind it.
"His deserves to be a lifetime of complete and utter silence."
Ardern praised the strength of the Muslim community for their words expressed in court in the past days.
"Nothing will take the pain away but I hope you feel the arms of New Zealand around you through this whole process.
"And I hope you continue to feel that through all the days that follow."
Tarrant admitted killing 51 people at two mosques last year and was sentenced today.
He initially pleaded not guilty to his offending but later admitted 51 charges of murder, 40 counts of attempted murder and one of engaging in a terrorist act laid under the Terrorism Suppression Act 2002.
Ardern said she felt "relief" when she heard the news of the sentence.
"This has been a crime in New Zealand the likes of which has never occurred before. And now we've seen a sentence the likes of which we've never seen before.
"It gave me relief to know that that person will never see the light of day."
It was up to the families to know whether justice was served today, she said.
She was also relieved to hear Tarrant didn't address the court today, and it was everyone's job to deprive him of notoriety.
"The offender achieved the opposite of what he intended because they [the Muslim community] have come out as a community stronger, supported by New Zealand."
She said she was privy to details of the attack that have only recently become public.
"There's very few additional things that could make an act seem any more despicable than it already was.
"What we've seen are extra details around an already a horrific, despicable act.
"That in itself is pretty horrific to know, how much went into causing this devastation."
National Party leader Judith Collins was pleased with the day's outcome.
"Seems like an appropriate sentence to me. I'm very pleased for the victims and their families," she told the Herald.
Greens' co-leader James Shaw said: "Our thoughts are with the affected communities and the families of the victims. I'm sure it is a great relief to them and to everyone in New Zealand. It is an entirely appropriate sentence."
Act leader David Seymour also said it was the "only appropriate sentence".
"I'm glad the judge gave it. My thoughts are with the victims and survivors."
Before today's sentencing Collins, a former Justice and Corrections Minister, said it was "tempting" to say Tarrant should be deported to serve his sentence in Australia.
"The problem with this ... is that Australia has when I last checked around 900 New Zealanders serving sentences in Australian jails," she said earlier today before the sentence was made public.
"Australia has always been keen to send us those 900 during the term of their sentence. That would mean New Zealand would either have a whole lot of criminals who have not served their sentences wandering around the communities, or else we'd have to find jail space for them.
"I'd be very wary sending him back at the moment. That's one practical reason why not."
Collins said she wanted to send a "big collective hug" to those people who read out their victim impact statements in the previous days.
"It is a really tough time and they will be reliving everything. But I know that they will feel much better for having had the opportunity to say what they want to say.
"I've certainly heard that from many victims over the years. It's really tough doing it, but they'll feel at least we've been listening."