Kensington Palace shared the announcement in a Tweet which read:
"The Duke and Duchess of Cambridge are delighted to announce that they have named their son Louis Arthur Charles.
"The baby will be known as His Royal Highness Prince Louis of Cambridge."
Prince Louis joins siblings Prince George, 4, and Princess Charlotte, who turns 3 in May.
The history behind the new royal baby's name: Louis Arthur Charles
Louis is one of the middle names of the baby prince's big brother, George, and is the name of an uncle of Prince Philip - Louis Mountbatten, 1st Earl Mountbatten of Burma
Arthur was a middle name of King George VI - the Queen's father, and the newborn's great grandfather.
Charles is of course the name of the prince's grandfather.
Prince William and Kate Middleton welcomed their third child on April 23 at 11:01, weighing in at 8lbs and 7oz.
Prince Louis is fifth in line to the throne.