The Duke and Duchess of Cambridge have named their third child Louis Arthur Charles.
The couple's second son was born at 11:01 BST on Monday at the Lindo Wing of St Mary's Hospital in London, weighing 8lb 7oz.
A tweet from Kensington Palace said the baby would be known as His Royal Highness Prince Louis of Cambridge (pronounced Lou-ee, not Lou-iss).
The new prince is fifth in line to the throne.
Louis is one of the middle names of Prince William and of the new prince's brother, George.
It was also the first name of Lord Mountbatten - his great-great-great uncle - who was killed by the IRA in 1979.
Lord Mountbatten had a strong influence in the upbringing of great-nephew Prince Charles and was described by the latter as "the grandfather I never had".
Arthur is also one of the duke's middle names, and was a middle name of King George VI - the Queen's father.
'A family favourite'
By Sarah Campbell, BBC royal correspondent
The pool of names considered suitable for a prince is not large and yet, the wait between birth and public naming suggests there was some indecision about what to call the new baby.
It did give punters four days to place their bets, though - and most of them will be disappointed.
Louis certainly wasn't the front-runner as far as the bookies were concerned, but it is clearly a family favourite.
William and George both have it as a middle name.
But with its French and German origins, it will no doubt generate some eyebrow-raising, Brexit-related comment.
There will also no doubt be some confusion over the pronunciation (Loo-ee not Loo-iss).
What is certain is that we are unlikely to see much of Prince Louis of Cambridge in the coming months and years.
His parents remain determined to bring up all three of their children away from the public's gaze as much as is possible.
Bookmakers had Arthur as the favourite name for the prince, followed by James and Philip.
Historian Judith Rowbotham said Louis is "not a traditional Windsor name" and a "little surprising" - but said it was still a safe choice for the royals.
"It's very much an acknowledgement of a wider heritage," Dr Rowbotham said, adding that it is also "very much an affectionate tribute" to the Prince of Wales, who was "deeply devoted" to Lord Mountbatten.
Former One Direction star Louis Tomlinson tweeted: "Young Louis welcome to the world. I'll take you under my wing lad. The Adidas tracksuit is in the post!"
Young Louis welcome to the world. I’ll take you under my wing lad. The Adidas tracksuit is in the post!— Louis Tomlinson (@Louis_Tomlinson) April 27, 2018
Louis is the 71st most popular name for a boy in England and Wales, according to the Office for National Statistics (ONS).
The name was 38th out of the top 100 baby names for boys in 2004 but has been declining in popularity.
In 2016, 911 newborn boys were named Louis by their parents compared to more than 5,000 who were named George.
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On Thursday evening, Prince William told reporters that they were still deciding on a name, saying: "I'm working on that."
Earlier in the week, he said Catherine and the baby were "in good form, luckily", and added: "Sleeping's going reasonably well so far, so he's behaving himself, which is good news."