"Welcome to our village wee one", she wrote, next to a picture of her and partner Clarke Gayford cuddling the newborn.
Her office confirmed the Prime Minister was in labour on Thursday morning, reportedly already four days past her due date.
Ardern, 37, took office as New Zealand's third female prime minister previous year and announced in January that she was expecting a baby with her partner, television fishing show presenter Clarke Gayford.
Ms Ardern has previously said she would take six weeks maternity leave.
Ardern and her partner Clarke Gayford have announced they have welcomed a healthy baby girl.
"Thank you so much for your best wishes and your kindness", Ms Ardern said.
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It is a habit drilled into citizens from a young age, with students expected to clean their school classrooms and hallways. He became the team's coach in 2015, and is now the only black head coach at the World Cup .
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The Green Party co-leaders have send their best wishes, saying it is historic moment for the country.
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.
Before she was elected previous year, Ms Ardern made headlines after criticising a radio show host for suggesting employers had a right to know if their female employees planned to have children, saying such questions, while appropriate for her in her position, were "totally unacceptable" for other women in a modern society.
The child is the first for Ardern and Gayford.
Prime Minister Ardern made the comments during her final press conference ahead of the baby's arrival.
Ardern has said there would be little disruption during her time off because she would stay in regular contact with Peters and be involved in major decisions.
Ms Ardern found out about the pregnancy last October and told Mr Gayford about the news through Facebook video call.