Thanks to a change agreed by the leaders of the Commonwealth countries in 2011 and passed into law this year, the baby's place in the order of succession would have been the same regardless of sex.
Previously, boys automatically trumped female siblings. So a first-born daughter could be pushed out of line by a younger brother.
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.
"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 royal birth is expected to be good for business.
The UK-based Centre for Retail Research estimates retailers will sell $121 million worth of royal-related baby toys and souvenirs. Merchandise ranges from diaper covers and clothing to a "prince potty chair," which of course is in the shape of a throne.
On Twitter, topics related to the royal baby jumped to the top of the trending list in the United Kingdom Monday morning. Worldwide, hashtags such as #RoyalBabyBoy and #Will & Kate were trending later in the day.
Many tweets were along the lines of the comment of Holly Thrift, who wrote, "The royal baby is coming! I am freaking out!"
The baby was the only topic on the radio talk show hosted by Vanessa Feltz on BBC London 94.9 on Monday morning.
But not everyone was thrilled. Feltz read on air a message from "Gary" asking, "Please, please please, I implore you not to devote too much of the morning's show to the royal baby."
Feltz replied, "C'mon, Gary, give an inch. .... It's huge, we can't ignore it."
She reported Gary sent another message: "OK, point taken. I'm a beaten man."