"Both my wife and I are overjoyed at the arrival of my first grandchild," a statement from the Prince of Wales read. "It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy.
"Grandparenthood is a unique moment in anyone's life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future."
Kate Middleton and Prince William welcomed a baby boy at 4:24pm at St Mary's Hospital in Paddington.
The news was greeted by huge cheers from the onlookers who had gathered outside the hospital and Buckingham Palace.
The baby boy weighed 8lb 6oz. Mother and baby are said to be doing well and Kate will remain in hospital overnight. The Duke of Cambridge was present at the birth, and is expected to spend the night with his wife and newborn son in the Lindo wing.
From early Monday morning when it was announced that the Duchess of Cambridge was in labour, Prince Charles was in a jolly mood. The future King spent the day on a public engagement in Yorkshire, happily accepting gifts for his grandchild.
Members of the public shouted "Congratulations" to Charles who had been visiting the glaziers' workshops.
He walked over to one woman, smiling, and said: "Do you know something I don't?"
Another well-wisher, John Dowson, from York, shouted: "It's triplets!", prompting Charles to chuckle and go over to him for a chat.
John said: "I felt like saying 'Congratulations, sir, it's triplets!' - just for a bit of fun. He just laughed. He was really jolly. Everybody's so excited in the country for him. Let's see what happens."
Watch all the action from outside the Lindo Wing as the world awaits news of the arrival of the Prince or Princess