New Zealand Prime Minister Jacinda Ardern carries her newborn baby Neve Te Aroha Ardern Gayford as she walks out of the Auckland Hospital in New Zealand, June 24, 2018.
Ms Ardern, 37, is only the second world leader to give birth while in office after former Pakistani Prime Minister Benazir Bhutto who delivered a baby girl in 1990.
Jacinda Ardern is New Zealand's first leader to give birth while in power.Ardern insists it will be business as usual during her six weeks off.
The couple have explained why they settled on Neve Te Aroha Ardern Gayford.
She and Mr Gayford had opted to spell the name Neve - as opposed to Niamh, for example - for simplicity, with Ms Ardern joking about the unusual spellings of Clarke and Jacinda.
While Ardern had been hailed as a pacesetter, and inspiration for women who wanted to have families and careers, Gayford had also been congratulated on his choice to take time off from his job to care for his daughter.
"Gosh those moments happen so quickly, I think every new parent will probably reflect that you want to really cherish it but it happens very very quickly", Ardern said.
"It means bright and radiant, and snow, which seem like a good combination for Matariki and for solstice".
"And that it's generally accepted, not just that women can make choices, but actually that men can too", Ardern added, referring to Gayford, who was standing beside her. She would be taking a six-week maternity leave, with Winston Peters serving as acting prime minister during that period.
"I won't forget the look on Jacinda's face when she finally held the baby", Mr Gayford said.
The couple announced the birth to the public on Instagram at 6.15pm that night.
"They congratulated the PM and Clarke and said they were looking forward to seeing them in the fall", the spokesperson said.
Feeling very lucky to have a healthy baby girl that arrived at 4.45pm weighing 3.31kg (7.3lb) Thank you so much for your best wishes and your kindness.
No doubt Ardern will appreciate returning to her own home, after hospital meals including Marmite on toast, porridge - and her midwife's macaroni cheese.
"Welcome to our village wee one", she captioned the photo.
Ardern appeared before dozens of reporters and a flurry of camera flashes at Auckland City Hospital in her first appearance since giving birth, thanking the public for their support as her three-day-old daughter slept in her arms.