After a tough week for women, Jacinda Ardern has just become Prime Minister of New Zealand.

The people of New Zealand finally know who will lead them after their federal election ended with no single-party majority almost a month ago.

New Zealand kingmaker Winston Peters says he will form a coalition with Labour, handing Jacinda Ardern the prime ministership.

It makes Ms Ardern, 37, New Zealand’s youngest Prime Minister. She will also be New Zealand’s third female leader.

Ms Ardern was first elected to NZ parliament in 2008 and has served as Opposition leader since August this year. The politician said she is “honoured, privileged and humbled” to become Prime Minister.

“The negotiations have been courteous, constructive and robust. Throughout, we have focused on our shared values and the policies that can take New Zealand forward,” she said.

“We are both committed to forming a strong and durable government that can deal with the many challenges this country faces.

“The Green Party is now undertaking its internal approval process before we confirm final arrangements to form a Labour-led progressive Government. This too has been an excellent process, which I thank James Shaw and his team for.”

The New Zealand First leader said in a statement on Wednesday night that he would make an announcement on which party he was going to form a coalition with on Thursday.

Going with National would have secured the government a fourth term in office.

Going with Labour makes Jacinda Ardern prime minister in a government that includes the Greens.

Australian opposition Leader Bill Shorten was quick to congratulate Ms Ardern.

“In electing their third woman to serve as prime minister, New Zealanders have again provided an inspiration for women and girls around the world,” he said in a statement.

The Turnbull government is yet to respond to the news.

There might be some initial awkwardness in Australian-New Zealand relations with Ms Ardern’s rise to power.

In August, Foreign Minister Julie Bishop accused New Zealand’s opposition Labour Party of conspiring to undermine her government.

She said Australia’s opposition Labor party had used its New Zealand counterpart to raise questions about Deputy Prime Minister Barnaby Joyce’s Kiwi citizenship in the New Zealand parliament.

“This is highly unethical at least but more importantly it puts at risk the relationship between the Australian government and the New Zealand government,” Ms Bishop said at the time.

“Should there be a change of government, I would find it very hard to build trust with those involved in allegations designed to undermine the government of Australia.”

Ms Ardern responded at the time the claims were false and “highly regrettable”.

She said she had contacted the Australian High Commission to register her disappointment and would be meeting the commissioner in person.

Labor’s foreign affairs spokeswoman Penny Wong said the Turnbull government must take immediate action to rebuild relations with the incoming New Zealand government following Ms Bishop’s attack on Ms Ardern.

“It is now incumbent on the foreign minister to undo the damage caused by her irresponsible remarks during the election campaign,” she said.

It was Senator Wong’s chief of staff who sparked the NZ Labour questioning.

Comment has been sought from Ms Bishop.