The couple married in April 2011 and have been watched closely since for any sign of producing a new heir to the throne.
"Their Royal Highnesses the Duke and Duchess of Cambridge are very pleased to announce that the Duchess of Cambridge is expecting a baby," the palace said in a statement. "The Queen, the Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall and Prince Harry and members of both families are delighted with the news."
ABC News said the duchess was admitted to London's King Edward VII Hospital to be treated for hyperemesis gravidarum, an acute morning sickness requiring supplementary hydration and nutrients.
"As the pregnancy is in its very early stages, Her Royal Highness is expected to stay in hospital for several days and will require a period of rest thereafter," the palace statement said.
When the baby is due and what its gender is were not reported.
White House press secretary Jay Carney wished the couple well during a media briefing Monday.
"[On] behalf of everyone here in the White House, beginning with the president and the first lady, we extend our congratulations to the Duke and Duchess of Cambridge on the welcome news this morning out of London, that they are expecting their first child," Carney said.
Asked if the president and first lady have any advice for them as parents, Carney replied, "I haven't had that conversation with them, but I know they both feel that having a child is one of the most wonderful parts of their lives, so I'm sure that will be the same for the Duke and Duchess of Cambridge."