"Welcome to our village wee one," Ardern wrote on Instagram at 6.15pm on Thursday.
Prime Minister Jacinda Ardern is in labour and has been admitted to Auckland City Hospital.
The Prime Minister's Office has confirmed Ardern, 37, arrived at hospital with her partner Clarke Gayford, at 5.50am. Gayford drove the couple to hospital in their own car as planned.
Deputy Prime Minister Winston Peters is now Acting Prime Minister.
When former Pakistan Prime Minister Benazir Bhutto gave birth to her daughter Bakhtawar on January, 25, 1990 she was the first modern head of government to give birth while in office. Bhutto was assassinated in 2007. Today would have been her 55th birthday.
Her daughter Bakhtawar Bhutto congratulated Ardern on her pregnancy via Twitter today.
"Congratulations to Prime Minister @jacindaardern on the wonderful news," she wrote.
Ardern's arrival has sent ripples of excitement around the hospital.
A doctor who works there says she heard about Ardern going into hospital on the radio.
She says she's excited for the Prime Minister and hopes she gets out of hospital soon.
A nurse who had just finished a night shift thought it was interesting that the Prime Minister was giving birth at the hospital amid all the controversy of industrial action.
She says it's exciting all the same and is wishing Ardern all the best.
Another man, who arrived at the hospital to visit a sick grandchild, said he was excited to know if Ardern would have a boy or a girl and wished her well.
There will be no further formal announcements from the Prime Minister's office until Ardern and Gayford, 40, announce the birth of their baby.
Auckland City Hospital says 6974 babies were born there last year.
"The average length of stay for a woman giving birth in our hospital is 2.3 days. Typically a woman will be discharged home or to Birthcare, depending on her requirements."
If born today Ardern and Gayford's baby would share a birthday with Prince William (who the couple met in Britain this year), actor Chris Pratt and singer Lana Del Rey. Their star sign is Cancer.
The irony that if anti-monarchist Jacinda Ardern's baby is born today, her child will share its birthday with the future King of England (and New Zealand). 👑🇬🇧🇳🇿😲🍼 #nzpol
The child's birth will be significant; given he or she is the first child born to a female New Zealand Prime Minister, in power, in our country's history.
Reckon #HilaryBarry might win Jacinda’s baby bet - today/boy
Prince William, 1982 Joko Widodo, Indonesia president, 1961 Lana Del Rey, musician, 1985 Edward Snowden, NSA whistleblower, 1983 Jean-Paul Sartre, French philosopher, 1905 Benazir Bhutto, former Pakistan prime minister and first female leader of a Muslim nation (also the first head of government to give birth while in office), 1953 Shirin Ebadi, Iranian lawyer and human rights activist and first Muslim woman to receive the Nobel Peace Prize (2003), 1947
Prime Minister of New Zealand @jacindaardern is in hospital right now giving birth to her first child.
Today is also the birthday of our hero Edward @Snowden.
All the stars are aligned for the birth of another truth-teller 😘
"I am thinking of Jacinda with so much excitement as she approaches giving birth for the first time," co-leader Marama Davidson said.
"Her and Clarke have my best wishes for this special experience.
"This is an exciting time for Jacinda and Clarke and a historic moment for our country," said James Shaw in reference to the fact that this will be the first time a Prime Minister in New Zealand has had a baby while in power.
"I join with Marama and our Green Party caucus colleagues in wishing them both all the best."
How the baby news was announced
In mid-January, Ardern shocked the country when she announced, via social media, that she was expecting.
"We thought 2017 was a big year. This year, we'll join the many parents who wear two hats. I'll be PM & a mum while Clarke will 'first man of fishing' & stay-at-home dad," the couple announced.
"There will be lots of questions [I can assure you we have a plan all ready to go] but for now bring on 2018.''
We thought 2017 was a big year! This year we’ll join the many parents who wear two hats. I’ll be PM & a mum while Clarke will be “first man of fishing” & stay at home dad. There will be lots of questions (I can assure you we have a plan all ready to go!) but for now bring on 2018 pic.twitter.com/nowAYOhAbF
"Congratulations Jacinda Ardern on your wonderful news today. When we spoke this morning you sounded more excited than you did when you won the election!"
Congratulations @jacindaardern on your wonderful news today. When we spoke this morning you sounded more excited than you did when you won the election! Lots of love and best wishes from me and Lucy and all of us across the ditch.
Former New Zealand prime ministers also came out in support, with both Jenny Shipley and Helen Clark offering congratulatory messages.
Some eagle-eyed Kiwis were quick to point out that now meant Clark was very much the real "aunty Helen".
Wishing @jacindaardern & @NZClarke all the best as they expect their 1st child in June: a super busy year coming up & much to look forward to. Every #woman should have the choice of combining family & career. https://t.co/Ma6B6OGXJe
Ardern has been well received at public events during her pregnancy and has travelled and appeared at many engagements over the past few months.
Her trip to Waitangi, in the lead-up to Waitangi Day, was widely regarded as one of the best appearances of any New Zealand leader in history.
She became the first female prime minister to speak at the upper marae and many remembered her walking around in barefoot and helping to serve the public a hearty breakfast alongside her Labour Party colleagues.
