He will be known as His Royal Highness Prince George of Cambridge.
They are currently at the duchess’s family home in Bucklebury, Berkshire, after spending a night at Kensington Palace.
The Duke and Duchess had been expected to pick a traditional royal name for their son, who was born at St Mary’s Hospital in London on Monday at 16:24 BST, weighing 8lbs 6oz.
Royal infants usually have historical names which are passed down through the generations.
This is a relatively quick announcement of a name compared to previous royal babies.
It was seven days before the name of a newborn Prince William was announced in 1982, and there was a wait of a month following the Prince Charles’s birth in 1948.
All births in England, Wales and Northern Ireland, regardless of parentage, must be registered within 42 days at the hospital before leaving or a register office.