A tweet from Kensington Palace confirmed the baby would be known as His Royal Highness Prince Louis of Cambridge.
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-uncle – who was killed by the IRA in 1979.
Arthur is also one of the duke’s middle names, and was a middle name of King George VI – the Queen’s father.