World leaders have begun sending messages of congratulations to William and Kate, welcoming the couple's new arrival.
In a statement, U.S. President Barack Obama said:
"Michelle and I are so pleased to congratulate The Duke and Duchess of Cambridge on the joyous occasion of the birth of their first child. We wish them all the happiness and blessings parenthood brings.
"The child enters the world at a time of promise and opportunity for our two nations.
"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."
Australian Prime Minister Kevin Rudd said today was "a happy day" for the countries of the Commonwealth:
"On behalf of all Australians, Therese and I extend our warmest regards to the new parents, Prince William, Duke of Cambridge and Catherine, Duchess of Cambridge.
"Prince William holds a special place in the hearts of many Australians. Some of us remember his first visit to this country as a 9-month-old baby more than 30 years ago with his mother Diana and father Charles.
"In more recent times, Prince William demonstrated deep compassion when he met with families in Victoria who had lost everything during the Black Saturday bushfires of February 2009.
"We share in the joy of the Royal Family, particularly Prince Charles on the birth of his grandson and Queen Elizabeth II on the birth of her great grandchild."
Canada's Prime Minister Stephen Harper offered "heartfelt congratulations" on his nation's behalf:
“This new beginning reminds us of the remarkable and enduring relationship our country has enjoyed with generations of the Royal Family.
"We recall with fondness the years of unfailing service by Her Majesty Queen Elizabeth II and His Royal Highness The Duke of Edinburgh and their deep affection for and loyalty to this country.
"We also recall the Royal Tour by The Duke and Duchess of Cambridge who were so warmly received in Canada only two years ago. We look forward to their return to Canada and to being able to introduce their child to Canada and all Canadians.
“Laureen and I send our best wishes of health and happiness to the new parents as they embark on this exciting chapter in their lives."