Prime Minister John Key has congratulated the Duke and Duchess of Cambridge on the birth of their first child.
Catherine, who was admitted to St Mary's Hospital in Paddington in the early stages of labour last night, gave birth to the boy with Prince William by her side. He weighs 8lb 6oz (3.9kg).
Mr Key said it was "wonderful news for Prince William and Catherine".
"The birth of a child is a time of great joy and excitement, and I know they will make excellent parents."
Mr Key also extended his congratulations to the Prince of Wales and Duchess of Cornwall, and the Queen and Prince Phillip, on the arrival of the newest member of the Royal Family.
"On behalf of the people of New Zealand, I wish Prince William, Catherine and the Royal Family all the very best," Mr Key said.
Mr Key said he hoped the baby would come to visit New Zealand.
A 21 gun salute was fired from Point Jerningham in Wellington at
midday to celebrate the birth.
The Governor-General Sir Jerry Mateparae also welcomed news of the birth of the Royal baby, saying the birth of a child is "always a time to celebrate".
"I'm sure I speak for everyone in New Zealand in saying that I look forward to the time when the Prince can come back to this country, and bring with him the Duchess and their new baby boy.
"In the meantime, as Governor-General, and on behalf of my wife Janine and all New Zealanders, I send our good wishes to the happy parents, Prince William and the Duchess of Cambridge, and to their families, on the birth of the Royal baby."
Labour Leader, David Shearer, also offered his congratulations to the royal couple.
"Whether you are royalty or not, becoming a parent is a life changing event. It is a time of joy, excitement and sleeplessness.
"Parenthood is a huge adventure. I wish Prince William and Catherine all the best as they get to know their baby, and adjust to life as a parent.
"I also want to pass on my congratulations to the Queen, who will no doubt be delighted at the birth of her grandson, who is now third in line to the throne," says David Shearer.
New Zealand gifted Prince William and Catherine a hand-spun, hand-knitted fine lace shawl, similar to the one that New Zealand gave when the prince was born.
Like Prince William's shawl, it was also designed by Margaret Stove. Cynthia Read spun the wool and knitted the shawl.
As well as the shawl, and with the blessing of the Duke and Duchess of Cambridge, an invitation was sent to knitters around the country to knit baby singlets to give to new parents at local maternity and neonatal units on the couple's behalf.
A number of buildings and landmarks in New Zealand will glow blue to celebrate the arrival.
The Baycourt Theatre in Tauranga will be one of the buildings
which will be lit up for the new royal baby boy from 5pm. In 1983
Princess Diana and Charles opened the building.
Auckland War Memorial Museum will also mark the birth of His Royal Highness Prince of Cambridge by lighting the exterior of the building blue.
Auckland Museum Director Roy Clare said: "It is a significant moment in Aotearoa New Zealand's constitutional history and public life and we are very pleased to contribute to the global celebrations by illuminating the museum in blue this evening."
Sisters Sue and Pauline, on holiday from New Zealand and Australia respectively, clad in their national flags told AAP they didn't want to miss a chance to be part of a "historic occasion".
The pair waited outside Buckingham Palace this morning, where a notice was placed in an easel announcing the birth.
"My sister always thought it was going to be born on Monday so
we were ready to come down," Sue said.
Sharing a royal birthday
While Prince William and Catherine enjoy getting to know their baby, a number of Kiwis will also have their own bundle arrive today.
Around 167 New Zealand babies will share their birth date with the future king, Statistics New Zealand said.
"Baby boys born today in New Zealand might expect to live 90 years on average, and girls 93 years," Acting Government Statistician Dallas Welch said.
If heredity is anything to go by, the royal baby has a good chance of living even longer than that. Queen Elizabeth II, the new prince's great-grandmother, is 87, and the Queen Mother lived to 102.
When Prince William, the new baby's proud father, was born in 1982, the New Zealand population was 3.2 million. Today New Zealand is nearing 4.5 million, and in another 30 years, when the new prince may be having his first child, Statistics New Zealand projects that the population could be around 5.6 million.