The Duchess of Cambridge left King Edward VII Hospital on Thursday.
Prince William was on hand to collect his wife, who will now head to Kensington Palace for a period of rest, said St James's Palace.
The Duchess, who is thought to be around eight weeks pregnant, was being treated for hyperemesis gravidarum, a rare condition which causes severe vomiting during pregnancy.
She emerged carrying a bouquet of yellow flowers and walked from the building with William. She gave a brief smile to the waiting press before being driven away with her husband.
Mel Grieg and Michael Christian of radio station 2Day FM convinced staff to put them through to the Duchess's private nurse.
Despite mimicking the corgis barking and putting on unconvincing English accents, the nurse replied to their questions, saying: "She's sleeping at the moment and has had an uneventful night, she's been given some fluids, she's stable at the moment."
Prince William is said to be "furious" about the prank.
John Lofthouse, chief executive of the hospital said he regretted the breach, but condemned the call as "journalistic trickery".
Lofthouse said: "I think this whole thing is pretty deplorable. Our nurses are caring, professional people trained to look after patients, not to cope with journalistic trickery of this sort."
He said there was no chance the Duchess could have received the call, adding: "Technically I think this was a breach of patient confidentiality, which I very much regret. Having said that, the information which was inadvertently revealed is already in the public domain."