He's also promised the tot - whose name was unveiled today as Louis Arthur Charles - one of his trademark Adidas tracksuits.
Taking to Twitter, he posted to his 33 million followers: "Young Louis welcome to the world. I’ll take you under my wing lad. The Adidas tracksuit is in the post!"
The 26-year-old, who is a father himself to a little boy called Freddie, posted on social media shortly after the official announcement from Kensington Palace.
The Duke and Duchess of Cambridge confirmed the newborn's name in a statement today.
The tot will officially be known as His Royal Highness Prince Louis Arthur Charles of the United Kingdom of Great Britain and Northern Ireland - though it's possible he'll be called Louis for short.
The newborn shares the name Louis with his brother George, and dad William, who both have the middle name Louis.
The Duchess gave birth to Prince Louis on Monday - St George's Day - and the tot is fifth is line to the throne and joins the couple's two other children, Prince George, four and Princess Charlotte, two.