Prime Minister Jacinda Ardern has gifted The Duke and Duchess of Cambridge a special New Zealand-themed romper, among other gifts.
A statement from Kensington Palace revealed Duchess Catherine delivered their third child, weighing 8lbs 7oz, at 11:01am on Monday morning.
While his name is not yet known, the infant is Prince William and the Duchess of Cambridge's third child together, joining Prince George, four, and two-year-old Princess Charlotte in the royal family.
Ms Ardern has formally congratulated the royal couple.
"I am sure that New Zealanders join with me in celebrating the birth of a new baby to such a close and loving family."
New Zealand's official gift to the couple will be a hand-crafted 100 percent wool baby blanket featuring a manuka flower and seed pod design, along with a selection of New Zealand children's books.
"I also gave a personal gift of hand-made rompers with buzzy bee lining, sewn by a family member."
The new child is fifth in line to the throne, behind father Prince William, grandfather Prince Charles, and his older siblings.
Duchess Kate was taken to the Lindo wing of St Mary's Hospital in central London at about 6am on Monday morning (local time), after suffering her first labour pains.
A 21-gun salute celebrating the birth was fired at 12pm from Wellington's Point Jerningham.