As well as Pippa, other family members are also thought to have been waiting at the palace to celebrate the birth.
Speaking outside the hospital earlier, an obviously moved Duchess of Cambridge said: "It's been very emotional. Any parent will know what this feeling is like."
The Duke of Cambridge had followed the steps his parents Charles and Diana took with him 31 years ago, when he was born there on June 21, 1982.
"He's a big boy, quite heavy. We're still working on a name," he told reporters.
"Well he has a good pair of lungs on him, that's for sure"
Confirming that the prince was overdue, William said: "I will remind him of his tardiness when he is older."
With a huge smile he then added: "He's got her looks thankfully" to which the Duchess responded "No, no, no I'm not sure about that."
The Duchess wore a lilac purple dress, with her long hair falling in waves around her face. The new father wore a blue open neck shirt rolled up to his sleeves with black trousers.
The couple then returned in to the hospital as William held his son, swaddled in a blanket, before bringing him out again in his car seat
William then breathed a huge sigh of relief when he successfully installed his baby on the back seat with his wife, before driving them home to Kensington Palace surrounded by a cheering crowd.
- DAILY MAIL