Oz's PM Rudd wishes 'royal bub' the best.
After Monday's announcement, the historic arrival was said to have been mentioned more than two million times on Twitter, while newspaper websites across the world brought the royal birth to the top of their home pages.
Australian prime minister Kevin Rudd wished the "royal bub" all the best on behalf of all Australians.
"This is a day of great joy," he said. "When a new bub comes into the world, any old day, any part of the world, it is frankly a time for rejoicing.
"To Prince Charles and Camilla, they have the delight of being grandparents,
all I can say is, this is probably one of the best experiences of your life and I'm sure they're going to have a wonderful time with the royal baby."
Stephen Harper, prime minister of Canada - where William and Kate carried out their first royal tour together - said Canadians were "delighted" to learn of the birth of their son and sent "heartfelt congratulations".
Meanwhile New Zealand's prime minister John Key said the nation's official gift to the royal couple is a hand-spun, hand-knitted fine lace shawl, similar to the one given when Prince William was born, and there will be a 21-gun salute fired from Point Jerningham, Wellington, to mark the occasion.