The Duke and Duchess had revealed Kate's pregnancy on Monday after she was admitted to the King Edward VII Hospital.
But the Duchess, 30, walked from the hospital this morning clutching a bunch of flowers, before stepping into a waiting car with her husband.
Asked about her condition by the waiting press outside, she said: "I'm feeling much better, thank you."
Kate, who is less than 12 weeks pregnant, was wrapped up against the cold in a coat and scarf.
She will now head to Kensington Palace for a period of rest, St James's Palace said.
The royal couple had said they are 'immensely grateful' for the good
wishes they have received since the much-talked about pregnancy was made
public.
William has been at his wife's bedside every day she has
been in hospital, and the Duchess has also received visits from sister
Pippa and her mother Carole.
The Duchess is likely to have been
on a drip so she can receive fluids intravenously to combat the effects
of dehydration caused by the condition known as hyperemesis gravidarum.
But she responded to treatment and smiled to photographers as she left the hospital before 11am on Thursday morning.
Kate's diary of engagements for this week have been cancelled to allow for the extensive rest she will need after being discharged.
