"Their Royal Highnesses The Duke and Duchess of Cambridge are delighted to confirm they are expecting a baby in April 2015," Kensington Palace said in a statement.
"The Duchess of Cambridge continues to be affected by hyperemisis gravidarum, but her condition is steadily improving," it said.
The 88-year-old Queen Elizabeth II has said she is "delighted" at the news that comes just a year after the birth of the couple's first child Prince George in July last year.
The 32-year-old Duchess' pregnancy had already been announced in September but the due date had not been released.
She will make her first public appearance tomorrow since her pregnancy was announced last month as she joins Prince William to officially welcome Singapore's President Tony Tan for his four-day visit to the UK.
The duchess will also attend the Wildlife Photographer of the Year awards ceremony at the Natural History Museum here.
The second royal baby in April 2015 is unlikely to generate as much excitement as its older sibling Prince George, because of the relatively smaller chance of him or her being the future king or queen of England.
It affects 3.5 per 1,000 pregnancies, causes severe vomiting and can lead to dehydration, weight loss and a build-up of toxins in the blood or urine, called ketosis.
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