"Their Royal Highnesses The Duke and Duchess of Cambridge are delighted to confirm they are expecting a baby in April 2015," a spokesperson for the couple said.
The statement also confirmed Kate is still suffering from acute morning sickness.
"The Duchess of Cambridge continues to be affected by hyperemesis gravidarum, but her condition is steadily improving," the palace added.
This news suggests Kate is now 12 weeks pregnant - and there has already been speculation that the royal baby's birth could coincide with the couple's fourth wedding anniversary on 29 April or the Queen's 89th birthday on 21 April.
"It would be fitting for the baby to be born on the Queen's birthday as Elizabeth is the favourite name too," William Hill spokesman, Rupert Adams, told OK! magazine.
Kate joined Prince William to formally welcome Singaporean president Tony Tan on Tuesday, when he arrived in London for a four-day visit.
The royal couple greeted the president and his wife Mary at London's Royal Garden Hotel close to their Kensington Palace apartments, two years after they first met the foreign leader during the Diamond Jubilee tour to south east Asia in 2012.
She wore a coat dress by Alexander McQueen for her first public appearance since announcing her pregnancy in September.
We're sure Kate's maternity style will continue to be flawless as she makes her return to the spotlight.
More:Have You Seen?
Suggested For You
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements. Learn more