Ms Ardern received a standing ovation at a meeting of her Labour Party.
She will head a three-way coalition with the Greens and nationalist party New Zealand First (NZF).
Ms Ardern, 37, emerged as the surprise new leader after weeks of negotiation following September's inconclusive election, which resulted in a hung parliament.
The incumbent National Party won 56 seats - two more than the Labour-Green bloc - but was unable to agree a governing coalition.
The coalition sees an uneasy alignment between the Greens and NZF, which have previously clashed over issues including immigration policy.
But Ms Ardern has denied her government is a "coalition of the losers" and says she is hopeful it will see out its term.
Detailed discussions on policy will take place next week but Ms Ardern promised a "government of change" in remarks on Friday.
She reiterated her support for a referendum on legalising personal cannabis use, saying she had "always been very open" about her opposition to criminalisation.
"On the flip side," she added, "I also have concerns around young people accessing a product which can clearly do harm and damage to them."
She said she wanted to hear New Zealanders' views and would consider carefully the wording of any referendum question.
Using cannabis remains illegal in most countries. However, possession of small quantities is legal in some US states, Canada, Colombia, South Africa, Spain and in Dutch coffee shops. In Uruguay, it is legal to grow, sell and consume marijuana.
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