Prime Minister Jacinda Ardern and partner Clarke Gayford have announced the birth of their baby girl on Instagram, saying they feel "very lucky".

Photo: Supplied

The baby arrived at 4.45pm on Thursday, weighing 3.31kg.

Ms Ardern said they were "all doing well" and thanked the team at Auckland City Hospital.

She also thanked everyone for their "best wishes and kindness".

In less than 20 minutes, her Instagram post received more than 24,000 likes.

Former Prime Minister Helen Clark told Checkpoint it was a great day for New Zealand.

"Really, both of them are very modern young parents. A fine example to young people in New Zealand.

"Jacinda's done it her way, what a remarkable story.

"She's taken it in her stride, New Zealanders have taken it in their stride ... all round I think we're showing huge maturity as a country with this."

Acting Prime Minister Winston Peters has also congratulated the new parents.

"Can I extend very best wishes to all the family at this very happy time," Mr Peters said.

"Like the rest of the country we welcome the news of the birth of a healthy baby and are naturally delighted for the new parents."

National Party leader Simon Bridges and his wife Natalie have offered their warm congratulations.

"Natalie and I are delighted for Jacinda and Clarke," he said.

"Being parents is a joy and a privilege and we are sure your new arrival will fill your lives with all the happiness our children have ours.

"Congratulations to you both. Our family wishes yours every happiness."

Green Party co-leader Marama Davidson said the Prime Minister having a baby while in office was a "symbolically significant moment" for New Zealand and women in particular.

"[It] sends an important message that caring for children is one of the most important jobs in the world," she said.

As a mum, Ms Davidson said her heart was "bursting with pride and love" for Ms Ardern and her whanau.

Colleagues and friends have also offered their congratulations on Twitter:

Congratulations @jacindaardern & @NZClarke on your baby girl. A new chapter for your family but no doubt, it'll be the most exciting one! — Phil Goff (@phil_goff) June 21, 2018

Wonderful news! Huge congrats to Prime Minister @jacindaardern and @NZClarke on the birth of their baby girl! A warm welcome to the world! Wishing the family health, happiness, and all joy in the world. Tēnā koe i tō tamāhine. Ngā mihi mahana. — Ambassador Brown (@USAmbNZ) June 21, 2018

Congratulations @jacindaardern & @NZClarke - I am truly delighted for you! — James Shaw (@jamespeshaw) June 21, 2018

I had a hunch she would be a girl! Congratulations @jacindaardern and @NZClarke. So happy for you all! Another wahine toa for Aotearoa. — Julie Anne Genter (@JulieAnneGenter) June 21, 2018

Ms Ardern was driven to hospital by Mr Gayford and arrived at 5.50am this morning.

New Zealand First leader and deputy Prime Minister Winston Peters is now acting Prime Minister.

Ms Ardern has previously said she would take six weeks maternity leave.

Her due date was Sunday 17 June.

It's Ms Ardern's first child, and her partner will be a stay-at-home father.

Ms Ardern found out about the pregnancy last October and told Mr Gayford about the news through Facebook video call.

The couple announced the pregnancy to the public on 19 January.

They were inundated with good wishes from the public, current and former politicians and attracted comment from media around the world.

Ms Ardern was gifted the name Waru at Ratana celebrations and the name Waimirirangi was offered at Waitangi Day celebrations if the baby was a girl.

Photo: AFP PHOTO / POOL / Daniel LEAL-OLIVAS

Ms Ardern is one of very few elected leaders to have give birth while in office.

The only other recorded instance in recent times was of Pakistan's Benazir Bhutto, who was elected Prime Minister in 1988 and in 1990 gave birth to her second child.

Prior to her, Queen Elizabeth II gave birth to Prince Andrew in 1960 and Prince Edward in 1964 after her ascension to the throne in 1952. Queen Victoria, Catherine the Great and Cleopatra also became mothers while being leaders of their states.