The child, whose gender has not been identified, will be a younger sibling to Prince George, 4, and two-year-old Princess Charlotte. A statement from the palace said that "the Queen and members of both families are delighted with the news."
Less than an hour after news of Middleton's pregnancy was revealed, the London-based bookmaker William Hill revealed odds on the royal baby's name. Currently Alice is the most popular choice, with odds at 8/1, followed by Elizabeth (10/1), James (12/1) and Arthur (12/1). The odds on gender are equal, at 10/11 for a boy and a girl, and the odds on the Duchess of Cambridge having twins are pretty high, at 33/1.
The oddsmakers clearly believe that there's a chance the newborn could be named after a former or current member of the royal family. Diana (the name of Prince William and Prince Harry's late mother) has been given odds of 16/1, Margaret (the name of the Queen's late sister) has been given odds of 20/1 and Charles (the name of the baby's grandfather) has been given odds of 25/1.
The name Donald has been given particularly high odds of 50/1, but William Hill did not elaborate on why that might be the case.
Bookmaker Ladbrokes has similar odds: Alice is 7/1, followed by Arthur (10/1), Victoria (10/1), Alexandra (12/1), Albert (14/1) and Phillip (14/1). The odds on Middleton having twins is 4/1 and triplets is 50/1.
"The early money suggests punters would love to see Kate and Wills welcome another little girl into their family, who is called Alice," Jessica Bridge, a spokesperson for Ladbrokes, said in a statement. "It should come as no surprise to see fairly normal yet regal names top the betting."