Both Dad, 35, andDuchess Kate, 36, listed their occupations as Prince and Princess of the United Kingdom.
"Along with many people around the globe, New Zealanders have witnessed and celebrated the joy that the Duke and Duchess of Cambridge have clearly found with their children Prince George and Princess Charlotte", Ardern said.
The baby is Britain's first Prince Louis in more than a century.
But interestingly, little Louis nearly wasn't a prince at all.
Just look at baby Louis trotting about - but staying close to mum, Tibet. Last year, they also marked the day in private. In their wedding in 2011, Kate had to repeat William's full name when reciting her vows.
The French embassy to London tweeted: "We're delighted that you've been given such a lovely French name!"
Even though the name Louis is generally associated with the now non-existent monarchy of France with King Louis' of France I-XVI, the name Louis has popped up in the British royal family from time to time.
Rafael Nadal rates the prospects of Stefanos Tsitsipas after Barcelona Open triumph
After the win, Nadal dived into a pool at the venue along with some of the tournament's ball boys and ball girls. The 63rd-ranked Tsitsipas was trying to become the first Greek to win an ATP Tour title.
"And I'm sure that she, her husband, and the older siblings, George and Charlotte, have real, as I say, joy at the birth of their little one".
In the meantime, things are sure looking up for William and Kate now that they have their third child.
The baby was born weighing eight pounds and seven ounces (3.8 kilogrammes) at 11:01 am (1001 GMT) on Monday with William, the Duke of Cambridge, present for the birth.
Kate and Wills named their third child after Louis Mountbatten, Prince Philip's uncle, who was killed by an IRA bomb in 1979. He was assassinated by Irish republicans when his boat was blown up on a fishing trip off the coast of County Sligo in the Republic of Ireland.
William, along with Louis' older brother, Prince George, share the middle name Louis, which is believed to be a tribute to Louis Mountbatten.
Yesterday, it was revealed the young royal was almost not a prince at all.