The Duke and Duchess of Cambridge have emerged from St Mary's Hospital in west London with their new baby son.
Walking out with their baby to cheers from staff and well wishers, Kate said it was "a special time for any parent".
Prince William said they were "still working on a name".
The couple then went back inside the private Lindo Wing and placed their son in a car seat. A few minutes later they came outside again and the duke drove his family home to Kensington Palace.
Speaking to reporters, the couple both said the experience was "very emotional".
They appeared relaxed and smiled as they walked out on to steps of the hospital shortly after 19:10 BST in front of a mass of photographers.
William later held his son and walked forward with his wife to speak to reporters.
He said: "He's got a good pair of lungs on him, that's for sure. He's a big boy, he's quite heavy. We are still working on a name so we will have that as soon as we can."
The Duke and Duchess of Cambrige present the new
He added: "It's the first time we have seen him really so we are having a proper chance to catch up."
The duchess, smiling as she held her son, said: "It's such a special time. I think any parent will know what this feeling feels like."
Speaking to the waiting crowd, Prince William said: "I'll remind him of his tardiness when he's a bit older.
"I know how long you've all been standing here so hopefully the hospital and you guys can all go back to normal now and we can go and look after him."
They also revealed William had done the first nappy change.
Earlier in the afternoon, the couple were visited at the hospital by the Prince of Wales and Duchess of Cornwall, and Kate's parents, Carole and Michael Middleton.
Prince Charles said the baby was "marvellous" while Mrs Middleton said he was "absolutely beautiful".
Speaking to reporters as she left the hospital, Mrs Middleton said: "We are so thrilled".
She added her first cuddle with her new grandson had been "amazing".
There has been no word yet on what the couple plan to name the prince and asked if she had been told or made any suggestions, Mrs Middleton said: "Absolutely not."
Prince William was at the hospital for the birth at 16:24 BST on Monday, and stayed with his wife and son, who weighed 8lb 6oz (3.8kg), overnight.
Kensington Palace said in a statement: "We would like to thank the staff at the Lindo Wing and the whole 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."
Meanwhile, the birth of the third in line to the throne was marked by gun salutes at Green Park and the Tower of London and the ringing of bells at Westminster Abbey.
And at Buckingham Palace, royal watchers and tourists queued in the rain to catch a glimpse of the bulletin announcing the arrival of the royal baby at 16:34 BST on Monday, which is being displayed on an easel.