The official announcement came from the royal London residence Clarence House, which also tweeted the news: "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," the statement continued.
Prime Minister David Cameron tweeted his congratulations to Kate and William: "I'm delighted by the happy news that they're expecting another baby."
Kate is said to be in around her 12th week of pregnancy. The announcement came earlier than would have been expected, because she's had to cancel some public engagements.
HG causes constant nausea and vomiting, and sometimes it leads to a hospital stay.
The duchess is being treated by doctors at home in Kensington Palace.
Is HG more or less likely in a second pregnancy if you've had it in the first one? "It's as likely -- you continue to have it in each subsequent pregnancy," says Daghni Rajasingam, MD, consultant obstetrician at St. Thomas' Hospital in London. "It tends to be of the same severity. So if you have it mildly the first time, you have it mildly the next time."
This means mothers-to-be with a history of HG and their doctors can be ready to treat the condition early: "You'll know what worked in the past, and you might use your own strategies to start off with," Rajasingam says.
When it comes to treating HG, "it starts with keeping the woman hydrated," she says, "and making sure nutritionally she is eating enough."
If the woman isn't drinking enough, she might need fluids through an IV. "We try to get on top of the nausea and vomiting using anti-sickness tablets (anti-nausea medication) that are very safe in pregnancy," Rajasingam says.
Rest and saving energy are also important, whether a royal or not: "Her engagements are slightly different to the general woman's engagements or work," she says. "If you have severe hyperemesis, where you're vomiting the whole time, then resting is a good thing."
HG can last longer than the first trimester, she says. "Most women have it in the first three months of pregnancy, and it'll get better. In the small group that continue to have it for the latter part of their pregnancy, it will stop when the baby and the placenta or afterbirth are delivered."
A mother-to-be may feel different about her second pregnancy, according to U.K. parenting charity NCT.
Although Kate will know what to expect in practical terms, some mums find there is less excitement about a second pregnancy.
The NCT stresses the importance of resting and eating well during a second pregnancy.
Support for the older child is important, too.
The royal couple's first baby-name choice saw George rise up the rankings to become the 10th most popular U.K. boys' name this year.
Bookmakers are already taking bets on the first name for George's little brother or sister.
Among the favorites are traditional royal names Elizabeth, Henry, Philip, and Victoria.