"The Duke and Duchess of Cambridge are very pleased to announce that The Duchess of Cambridge is expecting their second child," tweeted Clarence House.
A statement from Kensington Palace said that the Queen and members of the royal family are "delighted with the news".
As with her pregnancy with Prince George, the Duchess is suffering from acute morning sickness - hyperemesis gravidarum. She is being treated inside Kensington Palace this time, rather than a private hospital where press had previously waited outside for updates.
"We're immensely thrilled, it's great news, early days but I'm hoping that things settle down, she feels a bit better," said Prince William today during an official visit to open the Dickson Poon University of Oxford China Centre Building. His wife pulled out of the engagement due her sickness.
"She's feeling ok," he continued. "It's been a tricky few days, week or so. I'm going to go back and look after her now."
Kensington Palace said the Duchess's attendance at forthcoming events would be decided on a "case-by-case" basis.
She is scheduled to make her first official solo overseas tour to Malta from 20 September for two days.
"Their Royal Highnesses The Duke and Duchess of Cambridge are very pleased to announce that The Duchess of Cambridge is expecting their second child," read the statement.
"The Queen and members of both families are delighted with the news.
"As with her first pregnancy, The Duchess is suffering from Hyperemesis Gravidarum. Her Royal Highness will no longer accompany The Duke of Cambridge on their planned engagement in Oxford today. The Duchess is being treated by doctors at Kensington Palace."
The Duchess had not yet passed her 12-week point, but the couple decided to make an announcement because of forthcoming public engagements which are now uncertain.
"There are a number of forthcoming engagements so we took the decision to be fully open about it at this point," a palace spokeswoman said. "One is the forthcoming visit to Malta and a decision on that will be taken closer to the time."
David Cameron also tweeted his well wishes.
"Many congratulations to the Duke and Duchess of Cambridge. I'm delighted by the happy news that they're expecting another baby," he wrote.
The new baby will be the fourth in line to the throne. He or she will not become a monarch, assuming the same role as Prince Harry.
An infographic of Twitter mentions shows that the news was unsurprisingly most popular in the UK, with Australian cities Melbourne, Sydney, Perth and Adelaide also quick to tweet.
Some have questioned the timing of the couple's announcement, suggesting that it could sway the Scottish independence vote later this month.
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