Kate Middleton, the Duchess of Cambridge, gave birth to the royal couple’s third baby, a boy, at St Mary’s Hospital in London, at 11:01 BST.
The new prince, who was weighing 8lb 7oz at birth, is fifth in line to the UK throne.
Kate Middleton and her son, who is yet to be named, are “both doing well”, Kensington Palace said.
Members of both families had been informed and were “delighted with the news”.
According to Kensington Palace, the name of the baby would be announced in due course while a formal notice of the birth had been posted on the forecourt of Buckingham Palace.
Favorite names at the bookmakers include Arthur, Albert, Frederick, James and Philip.
PM Theresa May tweeted her “warmest congratulations” to Prince William and his wife.
Following a change in the law in 2013, Princess Charlotte keeps her place as fourth in line to the throne.
Previously, younger royal males would have taken precedence over older female siblings.
Kate Middleton was admitted to hospital shortly before 6AM on April 23 with the announcement of the birth coming shortly after 1PM.