Prime Minister Jacinda Ardern has revealed what the Government gave the Duke and Duchess of Sussex to congratulate them on the arrival of their new son.

Overnight Meghan Markle gave birth to their baby boy, who weighed in at 3.26kg, with the couple are yet to decide on a name.

While the royal family cannot accept material gifts, Jacinda Ardern told Mike Hosking New Zealand will be giving money to Little Sprouts, an organisation that puts together baby boxes for families which are facing tough circumstances.

The Prime Minister says we'll also be buying 10 trees through Trees That Count, which plants native trees.

"On behalf of all New Zealanders I want to pass on our congratulations to the Duke and Duchess of Sussex on the happy news of the birth of their baby son," Prime Minister Jacinda Ardern said.

"The birth of a baby is such an incredibly exciting time.

"We wish them all the best, and very much look forward to seeing them all in New Zealand somewhere down the track.

"In line with their request we have not sent a gift, but the Government is marking the birth with donations to two New Zealand child-centred charities.

"We will be making a donation of $1000 to Little Sprouts, which gives packs of baby and children items to families in need.

"We are also donating 10 trees to Trees for Kiwi Babies, for native tree planting events during Matariki 2019. These donations will celebrate all New Zealand babies, as well as the new Royal baby.

"I hope New Zealanders think those are suitable gifts on their behalf in recognition of the new baby," she added.

The royals' newborn is yet to be named, but bookies are putting their weight behind three traditional names including James, Edward and Arthur as the likely options.

However, the pair are forward-thinking royals and may decide to surprise everyone when naming their first child. Canadian-born Autumn Phillips, and husband Peter Phillips, opted for a non-traditional name for their daughter Savannah - the Queen's first great-grandchild - in 2010.

In the US, the most popular name is Liam for a baby boy. In the UK, the most popular name for a boy is Oliver.

Harry and Meghan's child, who will be seventh in line to the throne, is extremely unlikely ever to be king, meaning the couple have more freedom with their choices.

In comparison, the Duke and Duchess of Cambridge chose to give their children traditional names, picking George for their firstborn, who is likely to one day be king.