leading a chorus of well wishes.
Obama and his wife Michelle wished William and Kate "all the happiness and blessings parenthood brings."
"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 president said in a White House statement.
The as yet unnamed royal baby automatically becomes third in line not only to the national throne but the other Commonwealth realms that have the British monarch as their head of state.
There are currently 16, including Britain, though that number could dwindle in the decades before the newest royal in likely to assume the crown.
Australian Prime Minister Kevin Rudd hailed the birth of the future king as a happy day for all in the Commonwealth, saying Prince William holds a special place in Australian hearts.
The prince's wife Kate gave birth to a healthy male heir weighing 8lbs 6oz (3.8 kilos) in London on Monday, providing both Britain -- and Australia -- with a future monarch. "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," Rudd said in a statement.
"This is a happy day for our close friends in Britain and the Commonwealth." He added that "Prince William holds a special place in the hearts of many Australians", given he first visited Down Under as a nine-month-old baby more than 30 years ago, with Charles and Princess Diana.
Support for the royals in former British colony Australia remains strong, although debate flares periodically about whether ties to the monarchy should be cut and the nation become a republic.
A similar debate comes and goes in New Zealand, where Prime Minister John Key said the "wonderful news" of the royal birth would renew interest in the royals. He acknowledged that some people want the country to become a republic, but added: "I think that's quite a long way away."
New Zealand is sending the baby a shawl made from fine New Zealand wool, while a 21-gun salute was planned in the capital Wellington to mark the occasion.
Canada's governor general also sent congratulations on behalf of his Commonwealth nation to William and Kate.
In a statement, Governor General David Johnston said he and his wife Sharon "would like to extend our warmest congratulations" to the royal couple. Prime Minister Stephen Harper meanwhile tweeted: "On behalf of all Canadians, I offer our heartfelt congratulations to the Royal Couple & the entire Royal Family."
Toronto's CN tower and part of the Niagara Falls are to be bathed in blue light this evening to mark the birth. Officials also said they hoped Prince William and Kate would return to Canada with the baby, for a visit. The couple visited Canada on their first official foreign trip after marrying.
On Twitter, celebrities fell over each other with congratulatory messages.
"It's a boy! So happy for my cousin Kate and the future King of England!" tweeted US talk show host Ellen DeGeneres, recently informed by the New England Genealogical Society that she is indeed a distant relative of the future queen.
Fellow funny lady Joan Rivers quipped: "Congratulations to Kate & William on the birth of their baby boy! So relieved that his name won't include the words Ivy or Apple."
All-news channels such as CNN, Fox News and MSNBC interrupted their regular programming for live reports from correspondents on the ground in London.
Fox News, famous for its conservative editorial slant, pointed out that the British royal family enjoys "a higher approval rating" than Obama.