The Kensington Palace had already announced that Kate Middleton is pregnant to second royal child but Prince William - a proud soon-to-be-dad-of-two - made a public announcement during the opening of the $36.4 million China Centre in Oxford, wrote News.com.au.

"It's been a tricky few days - week or so - but obviously we're basically thrilled, it's great news, and early days. We're hoping things settle down and she feels a bit better."

The Sydney Morning Herald reported that The Duke of Cambridge came to the event alone as The Duchess of Cambridge had to stay in the palace due to hyperemesis gravidarum - a condition that also caused her to be in the hospital when she was pregnant with Prince George.

The official statement from Clarence House read: "Her Royal Highness will no longer accompany The Duke of Cambridge on their planned engagement in Oxford today. The Duchess of Cambridge is being treated by doctors at Kensington Palace."

Because Kate Middleton is pregnant, the second royal baby is fourth in line to the throne - after Prince Charles, Prince William, and Prince George. This makes Prince Harry in fifth.

The Kensington Palace made this announcement in their twitter account: "Their Royal Highnesses The Duke and Duchess of Cambridge are very pleased to announce that The Duchess of Cambridge is expecting their second child. The Queen and members of both families are delighted with the news."

It did not mention something about the due date but said that Kate was not yet at the 12-week mark.

Just hours after the official announcement that Kate Middleton is pregnant, bookmakers were already busy taking bets on the name and birth date of the second child. NBC News reported London-based William Hill offered "Alexander" as the most likely at 9 to 1.

Jessica Bridge of Ladbrokes told People that "The Royal Baby betting frenzy is back in full swing. With one correct gamble already in the bag, punters are quickly reinvesting their winnings on the couple having a second son called James."