The newborn Prince of Cambridge weighed in at 3.9 kilograms and it is understood the delivery was without complication.
A photographer first broke the news that Kate had entered hospital, tweeting that he had seen the convoy and the security, sending the Twitter-sphere into a frenzy.
Clarence House then confirmed, via their official Twitter account, that Catherine had been admitted to St Mary's hospital.
In keeping with royal protocol, details of the birth were delivered to Buckingham Palace a short time ago and displayed in the front courtyard on the same wooden easel used to announce Prince William's birth.
The palace said in a statement: "Her Royal Highness The Duchess of Cambridge was safely delivered of a son at 4.24pm. The baby weighs 8lbs 6oz. The Duke of Cambridge was present for the birth.
"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news.
Prince Charles has also released a statement saying that he was "enormously proud and happy to be a grandfather for the first time", adding that it was "an incredibly special moment for William and Catherine".
A Buckingham Palace spokesman said of the Queen's third great-grandchild: "The Queen and Duke of Edinburgh are delighted at the news."
One vital piece of information missing from the official notice is the baby's name. We'll have to wait a little bit longer to find out what the new royal will be named.
Prince William has just made a brief statement saying he could not be happier and he will spend the night in hospital with wife Catherine and their new baby son, who are both doing well. William will not be making an appearance outside the hospital tonight.