The pair appeared outside the hospital where the baby was delivered, introducing their new son to the world for the fist time.
Kate gave birth to the little boy, third in line to the throne, yesterday.
The little boy, whose name has not yet been announced, will hold the official title of ‘His Royal Highness Prince (insert name here!) of Cambridge'
Kate and William, both 31, are believed to be heading to Kensington Palace before relocating to live with Kate's immediate family in Berkshire for the first few weeks.
The couple released a statement today thanking staff and hospital visitors for their support and understanding. The message read '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.'
William's father, Charles, arrived at the hospital at 5.30pm with his wife Camilla to meet the baby for the first time.
Kate's parents, Carole and Mike Middleton, also visited the hospital earlier today telling fans 'he's absolutely beautiful' after visiting their first grandchild. They continued 'we are so thrilled. The first cuddle was amazing.'
There has been celebration across Britain since the announcement of the birth - at 8.30pm yesterday. The little boy weighed in at at 8lbs and 6oz.
The Duchess had a visit from her hairdresser this afternoon, prompting speculation and hope that today would be the day the world got to meet the future King.
She was also visited by her doctor, Marcus Setchell, who visited at 8.30am to check-in on the new mother.
New grandfather Charles revealed this morning that he had 'no idea' what the little boy was named though he admitted he celebrated the arrival of his first grandchild by opening a bottle of champagne last night.