Heads of state from across the world are sending their best wishes to Kate and William following the keenly expected birth of their baby boy.

"I'm sure that right across the country and indeed right across the commonwealth, people will be celebrating and wishing the royal couple well," said British Prime Minister David Cameron.

"It is an important moment in the life of our nation, but I suppose above all, it's a wonderful moment for a warm and loving couple who got a brand new baby boy," he said.

Canadian Prime Minister Stephen Harper offered his country's congratulations.

"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 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."

The baby was delivered at 16:24 BST at St Mary's Hospital in Paddington, west London, weighing 8lb 6oz.

The Duke of Cambridge said in a statement the couple "could not be happier". He and the duchess will remain in the hospital overnight.

The news has been displayed on an easel in the forecourt of Buckingham Palace in line with tradition.

The new baby is third in line to the throne after Prince Charles and Prince William.