Ardern was admitted to hospital in Auckland for the birth of her first child on Thursday, according to a statement from her office.
Her office confirmed she had arrived at the hospital with partner Clarke Gayford.
Ardern, 37, became New Zealand's youngest Prime Minister when she took office through a coalition deal previous year after an inconclusive election, and now becomes the first woman in the country's history to give birth while in office.
Ardern will follow in the footsteps of the late Pakistan prime minister Benazir Bhutto, who in 1990 became the only women in recorded history to give birth while in power.
Ms Ardern has previously said she would take six weeks maternity leave.
The 37-year-old, who was elected in October, announced her pregnancy in January via Instagram.
"The birth has been highly anticipated in the South Pacific nation of almost 5 million people, and Ardern has continued to work right up until the birth, with her partner posting on social media on Wednesday afternoon a photo of her poring over official documents from home with the hashtag "#stillwaiting".
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The PM was four days past her due date, which was June 17.
"We wanted a family but weren't sure it would happen for us, which has made this news unexpected but exciting", she said in a statement at the time.
The much-anticipated arrival has gone global, as worldwide media outlets keep track of what is unfolding at Auckland Hospital.
Prime Minister Jacinda Ardern and Clarke Gayford arrive at Buckingham Palace during the Commonwealth Heads of Government Meeting (CHOGM) in London, April 2018.
"It makes a little bit more sense for me to be grounded in one place from now on", she said at the time.
Ms Ardern addresses parliament in Wellington.