The Prime Minister has said the birth of the royal baby is an "important moment in the life of our nation."
Mr Cameron said: "Its wonderful news from St.Mary's Paddington and I'm sure right across the country and indeed across the Commonwealth people will be celebrating and wishing the Royal couple well.
"It is an important moment in the life of our nation, but I suppose above all its a wonderful moment for a warm and loving couple who got a brand new baby boy.
"It's been a remarkable few years for our royal family - a Royal wedding captured peoples hearts, that extraordinary, magnificent Jubilee and now this royal birth.
"All from a family that have given this nation so much incredible service and they can know a proud nation is celebrating with a very proud and happy couple tonight. "
The royal baby appeared to wave as he was introduced to the crowds outside the hospital for the first time.
The Duke and Duchess of Cambridge proudly showed the world their baby son, a future king, before taking him home tonight.