Government and opposition politicians wished Ardern well, when news broke that she had gone to hospital early this morning.
Ardern is the second elected world leader to give birth in office. Opposition leader Bill Shorten retweeted Mr Gayford's photo with a congratulations.
Ardern, age 37, is just the second elected world leader to give birth while in office, and the first in almost three decades to do so.
Ardern became prime minister in October, making her the country's youngest premier since 1856.
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Ardern was keeping busy in the days leading up to her labour.
It was even more surprising given she had ruled out wanting to take the leadership, partly because it could affect her chances of having children.
Pakistan's Benazir Bhutto was the first world leader to give birth in office, in Pakistan.
The couple announced at the start of 2018 that they were expecting their first child in June.
"It's really exciting. I'm so happy for Jacinda and Clarke". She then continued to work from her home in Auckland up until the day before going into labor.
Ms Ardern is expected to take six weeks maternity leave before returning to her full duties.
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Ms Ardern's father Ross Ardern and mother Laurell were among the first visitors to meet the addition, who is their third grandchild.
She has said that she will still be on major decisions, such as issues of national security, and will keep reading briefings while she is off, but will leave the day-to-day running of government to Peters.
"The prime minister having a baby while in office is a symbolically significant moment for our country, women in particular, and sends an important message that caring for children is one of the most important jobs in the world", said Davidson. She led the group for three months before being elected Prime Minister.
Ardern's office confirmed just after 6 a.m. she'd arrived at the hospital with partner Clarke Gayford.
She said that after the birth, she hoped to have some quiet time to enjoy as a family.
"For New Zealand, these events and the way our country has greeted them will be seen as inspirational by all who advocate for gender equality and women's empowerment", Clark wrote.
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