Kate Middleton and Prince William Introduce Their New Daughter

Hours after her birth, the Royal Family's new princess has been presented to the world.

Swaddled in a white blanket and wearing a knitted pale yellow cap, the newborn slept through the whole debut. But that didn't stop her parents from flashing their bright smiles for everyone outside St. Mary's Hospital in London. Kate, who was holding her new baby, looked great in a silk yellow shift dress by Jenny Packham with nude pumps.

After giving birth earlier this morning (May 2), Kate and baby left the hospital later in the afternoon. After posing for photos, the couple then got into a black Range Rover and headed back to their home in Kensington Palace.

Before leaving, Prince William made a quick trip back home to get their one-year-old son, George, to visit his new little sister. Matching his dad in a blue sweater and white collared shirt, the little boy waved for photographers as Will carried him into the hospital. You can see the adorable moment below.

The couple also thanked everyone for their support via Twitter.

Prince William was reportedly hoping that the new bundle of joy would be a girl and is ecstatic about his growing family. "I know Prince William will be absolutely delighted," royal expert Katie Nicholl told Us Weekly. "He has secretly wanted a little girl. He wanted a girl [since] Prince George's [birth]. And I think it's wonderful. Now they have one of each."

And as the fourth in line for the throne, the birth of Kate and Will's daughter is a very important and historic one for the the British monarchy. "This will be the first princess for Cambridge for about 180 years," Nicholl said. "There's a real historical significance to this baby."

As previously reported, the name of the infant is still unknown and will be announced in the near future.