First full day dawns for Jacinda Ardern and Clarke Gayford's baby girl as addition to NZ's first family sparks celebration at home and world headlines

Prime Minister Jacinda Ardern has given birth to a healthy baby girl, sparking celebration at home and headlines around the world.

"Welcome to our village wee one," the 37-year-old politician posted on social media last night, having been driven to hospital in the morning by partner Clarke Gayford.

The baby - the couple's first - was born at 4.45pm weighing 3.31kg (7.3lb) and both mother and child were doing well, Ms Ardern's office said.

"I'm sure we're going through all of the emotions new parents go through, but at the same time feeling so grateful for all the kindness and best wishes from so many people," she said in a statement.

There was no mention of a name, although Ms Ardern earlier warned the couple were struggling to pick one.

A crowd of reporters had been gathering at the public Auckland Hospital since the morning, but the family are not expected to address media until at least today.

Ms Ardern now becomes the first elected world leader to take maternity leave - and only the second to have a child while in office - having handed over her duties to her deputy earlier in the day.

She is expected to take six weeks off.

The announcement of the birth spurred celebrations and an immediate outpouring of congratulations on social media and across the political spectrum.

Former prime minister and senior UN official Helen Clark described it as "inspirational", while the leader of the opposition, Simon Bridges, said he was delighted for the new parents.

Meanwhile major media organisations in the United States, Britain, Australia, Europe and Asia launched breaking news banners with the announcement.

Australian Prime Minister Malcolm Turnbull told the ABC he was "really thrilled", while Britain's Labour leader Jeremy Corbyn also sent his congratulations.

British Prime Minister Theresa May retweeted Clarke Gayford's announcement of the birth and added, "Congratulations to @JacindaArdern and @NZClarke on the birth of your little girl."   

For her part, Ms Ardern has played down the global attention she's received as a role model in recent months.

"I am able to do what I'm doing because I have enormous support around me and it makes me quite privileged," she said recently.

Determined to keep working until the final moment, Ms Ardern travelled until last week and her office yesterday confirmed she was still texting staff after going into labour to make sure they were fine.

Baby shares birthday with Benazir Bhutto and Prince William

Born on June 21, her baby will share a birthday with Pakistani prime minister Benazir Bhutto, the only other elected leader to have a child while in power. It's also Prince William's birthday.

The pregnancy news late last year came as a surprise to the Labour Party leader, who had to simultaneously deal with both intense negotiations to form a government and morning sickness.

Ms Ardern has since faced a stream of personal questions, parenting advice and media attention.

Recently, she has been talking down her coming absence from politics, assuring her country it'll be business as usual during time off.

While her day-to-do duties will now be handled by Deputy Prime Minister Winston Peters, 73, Ms Ardern will be on call for any major decisions.

Mr Gayford, 40, will be the child's primary carer after the Prime Minister returns to Parliament.