07/23/2013 02:24 EDT | Updated 07/24/2013 07:52 EDT

Royal Baby Photo: Duke And Duchess Of Cambridge Leave St. Mary's Hospital With New Son

We finally got our first look at the royal baby!

A beaming Duke and Duchess of Cambridge posed with their newborn son outside the Lindo Wing of St. Mary's Hospital on Tuesday, in front of throngs of admirers and the world media.

Kate Middleton, who gave birth to England's newest Prince on Monday, looked happy and healthy with her firstborn child in her arms. Wearing a blue and white polka dot blue frock, the Duchess was well on her way to becoming a stylish yummy mummy.

The baby, whose name is yet to be revealed, had a hint of fuzz on his head and was swaddled in a cute white blanket (Baby's first photo shoot!).

Prince William joked that his son was a looker. "He's a big boy, he's quite heavy. But we're still working on a name... He has way more hair than me, thank God...He's got [Kate's] looks, thankfully" said Will, who also mentioned that the birth of his first born child was "very special."

Kate also expressed her wonder about her baby boy: "It was very emotional, it is such a special time... It’s a moment that any parent having just given birth will know what this feeling feels like."

The royal tot better get used to the limelight now; the third-in-line to the throne will be living a public life alongside his famous parents, who definitely aren't camera-shy. We're sure Duchess Kate, Wills and Uncle Harry will have plenty of tips on dos and don'ts on how to behave in public. (Lesson No. 1: Don't play strip poker in Las Vegas!)

We bet the sure-to-be exhausted and excited parents will take their bundle of joy to meet great-grandparents, Queen Elizabeth II and Prince Phillip at Buckingham Palace and then will take up residence in their apartment.

The Middletons visited their daughter earlier on Tuesday, calling their first grandson "absolutely beautiful" while Prince Charles and wife Camilla, Duchess of Cornwall followed soon after. On Monday, Prince William and Harry's dad said:

“Both my wife and I are overjoyed at the arrival of my first grandchild. It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy."

For their part, the proud parents thanked St. Mary's for their help, saying:

"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."

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