- Prince Charles is "thrilled" by the prospect of becoming a grandfather
- Catherine is escorted from the hospital by her husband, Britain's Prince William
- She will now undertake a period of rest, a palace spokesman said
- Their child will be next in line to the British throne after William
She emerged from the hospital accompanied by her husband, Prince William, and carrying a bouquet of yellow roses, and was driven away by a waiting car.
A St. James's Palace spokesman said: "The Duchess of Cambridge has been discharged from the King Edward VII Hospital and will now head to Kensington Palace for a period of rest.
"Their Royal Highnesses would like to thank the staff at the hospital for the care and treatment the Duchess has received."
On her way out, Catherine acknowledged the crowd of reporters who have been camped outside the hospital since she was admitted Monday with hyperemesis gravidarum, a condition that involves nausea and vomiting more severe than the typical morning sickness many women suffer during early pregnancy.
Her hospitalization prompted the early announcement of her pregnancy.
In his first public comments since then, Prince Charles, the heir to the British throne, said he was "thrilled" by the news.
"It's a very nice thought to become a grandfather in my old age, if I can say so," he told reporters in London. "I'm very glad my daughter-in-law is getting better. Thank goodness!"
He also made a humorous reference to a story that dominated the UK headlines Wednesday, involving two Australian DJs who made a prank call to the hospital in which they impersonated Queen Elizabeth II and Prince Charles.
"How do you know I'm not a radio station?" the prince joked.
The hospital said it deeply regretted that the hoax call had been transferred to a ward in the early hours of Tuesday morning and a short conversation was held with one of the nursing staff.
The conversation included some general details of the duchess's condition and care, according to audio posted online by the DJs' Sydney-based radio station, 2Day FM.
2Day FM apologized Wednesday for a prank it said was "done with light-hearted intentions."
The duchess is not yet 12 weeks pregnant, Clarence House told CNN on Monday, so the palace is not announcing a due date for the child. Confirmation of the pregnancy followed months of speculation among royalty-watchers.
William and Catherine's child will be next in line to the British throne after William, regardless of whether it is a boy or a girl.
Planned changes to the law of succession that end the tradition of a boy taking precedence over an elder sister are already de facto in effect, the British Cabinet Office said.
William and Catherine were married at Westminster Abbey on April 29, 2011, in London's biggest royal wedding in three decades.
Their baby would be the first grandchild of Prince Charles and the late Diana, Princess of Wales.