Tributes around the world
The British monarch is also head of state in 15 Commonwealth countries, including Australia, Canada, New Zealand, Belize and Jamaica.
Canadian Prime Minister Stephen Harper offered his country's congratulations on the birth of a future king.
"The arrival of the newest member of the Royal Family, a future Sovereign of Canada, is a highly anticipated moment for Canadians given the special and warm relationship that we share with our Royal Family," he said in a statement.
Barack and Michelle Obama also gave their best wishes.
"The child enters the world at a time of promise and opportunity for our two nations," the U.S. president and first lady said in a statement. "Given the special relationship between us, the American people are pleased to join with the people of the United Kingdom as they celebrate the birth of the young prince."
Russia's President Vladimir Putin and Japan's Prime Minister Shinzo Abe also sent their congratulations.
On Twitter, topics related to the royal baby jumped to the top of the trending list in the United Kingdom on Monday morning. Worldwide, hashtags such as #RoyalBabyBoy and #Will & Kate were trending later Monday.
In a nod to modern times, Clarence House called for people to send news and images of any other new arrivals using the hashtag #WelcometotheWorld.