Ms Ardern went into labour on Thursday morning and gave birth to a healthy baby girl weighing 3.31kg (7.3lb) at 4.45pm.
Her office says both mum and the baby are doing well.
New Zealand Prime Minister Jacinda Ardern is seen with her baby daughter and partner Clarke Gayford at Auckland City Hospital, in Auckland, New Zealand June 21, 2018.
New Zealand Prime Minister Jacinda Ardern gave birth to a daughter Thursday and posted a message welcoming the healthy newborn "to our village".
Ms Ardern's due date was 17 June. She did not disclose the gender before the birth.
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"As a mum, my heart is bursting with pride and love for the prime minister and her whānau and wish them the very best for their future. 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.
When no party won sufficient support in the election to form a government, she was anointed prime minister by New Zealand First leader Winston Peters, the kingmaker in a three-party coalition also involving the Greens.
She points out that Ardern has pointed all naysayers wrong and, alongside stay-at-home dad Gayford, she is redefining the family stereotype and showing that maybe women can have it all.
The first female prime minister was Sirima Bandaranaike, who was elected to lead Sri Lanka (then Ceylon) in 1960.
On the campaign trail, Ardern, 37, had pushed back against questions about whether she meant to start a family, saying pregnancy should not affect a woman's career opportunities.
Clark wrote in the opinion piece that the couple's new baby has "considerable significance" for the country as a whole.