The Duchess of Cambridge, 30, mouthed "much better" and nodded when she was asked by the waiting international media if her condition had improved, before the couple were driven away by a security team.
Kate will now have a "period of rest" at Kensington Palace in central London where the couple have an apartment, said a statement from their office at St James's Palace.
"Their Royal Highnesses would like to thank the staff at the hospital for the care and treatment The Duchess has received," the statement said.
Kate was admitted to hospital on Monday with hyperemesis gravidarum, a severe form of morning sickness that affects about one in 200 pregnant women and is sometimes associated with twins.
Treatment for the condition usually involves hydration and nutrition as sufferers find it difficult to keep down any food or drink.
The pregnancy, which was only announced after she went to hospital, is believed to have not yet reached the 12th week. It will be the first child for the couple who married in April 2011.
The baby will be third in line to the British throne following last year's historic agreement among Commonwealth realms to end the practice of male primogeniture.
The hospital, a favourite with the royal family for decades, apologised on Wednesday after a nurse unwittingly released Kate's private medical details to hoax callers from an Australian radio station.
Sydney's 2Day FM station also said sorry after two presenters posing as Queen Elizabeth II and William's father Prince Charles, got through despite their poor imitations of English accents.
Hospital chief executive John Lofthouse said it was considering legal action.
"I've received advice that what the Australian broadcasters did may well have broken the law," he said. "On the other hand they've apologised for it so we're going to have a long and careful think about what, if anything, we do."
He said the hospital "deeply regretted" that the nurse had given away details of Kate's condition.
In the recording of the hoax call, the nurse can be heard saying about the Duchess: "She hasn't had any retching with me since I've been on duty and she has been sleeping on and off."
The Australian radio station was milking the publicity Thursday by boasting of the "biggest royal prank ever", despite an earlier apology by presenters Mel Greig and Michael Christian.
"We were very surprised that our call was put through. We thought we'd be hung up on as soon as they heard our terrible accents," the presenters said in a statement.
"We're very sorry if we've caused any issues and we're glad to hear that Kate is doing well."
The hoax is deeply embarrassing for the hospital, which has also treated the queen, her husband Prince Philip and Charles' wife Camilla over the years. The queen is its patron.
William, the second in line to the throne after Charles, visited Kate in hospital every day, spending hours at her bedside. Kate's younger siblings Pippa and James also paid her a visit on Wednesday.
William's own plans as his wife recovers are uncertain. The Royal Air Force search and rescue helicopter pilot is reportedly due back at his base in Wales next week but it is possible he may decide to stay in London.
He is due to attend a charity gala at London's Royal Albert Hall on Saturday, while Kate has cancelled all engagements for the coming days.
Speculation about her pregnancy has been intense ever since the couple married in a globally televised event in London's Westminster Abbey on April 29, 2011.MORE ON THE ROYAL BABY
Prince William and Kate Middleton’s baby could be named after Princess Diana
Daddy-to-be Prince William could name his little princess Diana, in loving memory of his mother, according to one expert.
Royal Author Phil Dampier said that he would be “astonished” if Kate and William did not use Princess Diana’s name for their first-born, if they were to have a royal baby girl, the Mirror reported.
Diana was one the most popular choice and Dampier believes the couple will no doubt be thinking about some sort of tribute to Princes William and Harry’s late mother, who died in a car crash in Paris in 1997.
Princess Diana (Photo: Getty Images)
“I think Diana’s influence will be very strong. Kate will surely have asked William about his upbringing and on their engagement Kate spoke about her regret at not meeting Diana and how she found her an inspiration,” Dampier said.
“I’m sure she will be looking at what Diana did as a mother and learning from her. I would be utterly astonished if Diana didn’t make up some part of the name should the baby be a girl.
“William missed her at the abbey when he wed Kate – she is always in his mind,” he added.
William-Kate’s baby to inherit throne regardless of gender
The royal baby due next year to the Duke and Duchess of Cambridge will ultimately accede to the throne regardless of its sex after changes in the rules of Royal succession, according to ministers.
In a break with more than 300 years of English constitutional tradition, laws that would have passed the Crown to the oldest male heir will not apply, the Telegraph reported. HEIR APPARENT
Kate Middleton, Duchess of Cambridge expecting twins?
The Duchess of Cambridge, who is expecting her first child with Prince William, maybe pregnant with twins, according to reports.
Kate, who has been admitted to the King Edward VII Hospital in London after she got ill while staying with her parents in Bucklebury, Berkshire, is suffering from hyperemesis gravidarum, a condition that is more often experienced by women expecting twins, the Telegraph reported. ROYAL TWINS
(With additional inputs)