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Kensington Palace said in a statement that Kate, who gave birth to the prince on Monday, will be discharged from London's St Mary's Hospital later on Tuesday evening.
William and Kate will take their son to Kensington Palace from the hospital, the palace added.
Crowds of journalists and onlookers camped outside the hospital are eagerly anticipating the baby's first public appearance.
Earlier, grandparents Prince Charles, his wife, Camilla, and Michael and Carole Middleton - Kate's parents - visited the young family at the hospital.
Charles called the baby "marvellous", and told reporters that "wait and see, you'll see him in a minute".
Carole Middleton described the infant as "absolutely beautiful".
The couple's Kensington Palace office said Kate, the Duchess of Cambridge, gave birth to the 3.8kg baby boy at 16:24 on Monday, triggering an impromptu party outside Buckingham Palace and in front of the hospital's private Lindo Wing.
The palace said Ton uesday that "mother, son and father are all doing well this morning".
As celebratory lights, gun salutes and other tributes were unleashed in Britain and abroad, William thanked staff at St Mary's Hospital "for the tremendous care the three of us have received".
"We know it has been a very busy period for the hospital and we would like to thank everyone - staff, patients and visitors - for their understanding during this time," he said in a statement.
