Prince Edward and the Countess of Wessex have named their new baby son James, Buckingham Palace has announced.
The boy, who is eighth in line to the throne, was born on Monday weighing 6lbs 2oz (2.8kg).
James Alexander Philip Theo Mountbatten-Windsor is a baby brother for four-year-old Lady Louise Windsor.
Buckingham Palace said both the Queen and Sophie's father were consulted over the names, and a spokesman said that both "are content".
Earlier, Prince Edward had said the couple planned to wait to choose a name until getting to know their son - whose title will be Viscount Severn.
Prince Edward and Sophie, 42, took him home from Frimley Park NHS hospital in Surrey on Thursday.
James was the name of five kings of Scotland and then a sixth who became James I of England at the union of the two countries in 1603. James II was born in 1633.
Is is understood to ahve been chosen because it is a favourite name of the couple, as is Alexander.
Philip is thought to be as a gesture to the Duke of Edinburgh, the baby's paternal grandfather, and Theo is a name shared with the baby's maternal great-grandfather.
Prince Edward and Sophie were much quicker naming James compared with his older sister Lady Louise in 2003, when they kept people guessing for more than two weeks.
As the couple's eldest son, his title is Viscount Severn or Lord Severn. His full surname is Mountbatten-Windsor, but he will only use Windsor.