Prince William and Princess Kate Introduce Their Baby Girl

The couple stepped out with their children as they left St. Mary's Hospital Saturday evening

Photo: Matt Dunham/AP

Standing proudly on the steps of St. Mary’s Hospital, Princess Kate and Prince William could not help but beam as they gave the world the first glimpse of their precious baby princess.

Wrapped in a white shawl from GH Hurt and Son Ltd. and an ivory bonnet and nestled in her mother’s arms, her royal highness contentedly slept through her introduction.

“We’re very happy, very happy,” William said when he first emerged from the hospital.

Just 12 hours after being admitted – and only 10 hours after giving birth to her 8-lbs., 3-oz. daughter – Kate looked stunning and remarkably groomed after a visit from Amanda Cook Tucker, the hairdresser responsible for her lustrous locks.

Barely showing any sign of the quick labor she had just endured, Kate donned a bespoke silk shift dress with buttercup print by Jenny Packham – the same designer behind the famous blue spotted frock she wore after Prince George’s birth.

The new princess’s shawl, meanwhile, has strong connections to the royal family. Other members have been presented with these shawls in the past and Princes George and William had a similar shawls when they were babies.

While they both smiled and waved to the crowd, Kate and William stayed just a few moments without making any comment before making their way home with William behind the wheel of a black Range Rover.

The little girl’s name is still unknown, and just like with George, it could only be announced after her great-grandmother, the Queen, meets her.

In a day of drama, Kate, 33, had made a dawn dash to the London hospital from her home at Apartment 1A at Kensington Palace, with William, 32, by her side.

Just three hours later, at 8:34 a.m., the baby girl made her arrival and the proud parents spent the morning calling their loved ones before an official statement was released at 11 a.m.

Before leaving the hospital, the couple thanked hospital staff. In a statement, Kensington Palace said, “Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have all received. They would also like to thank everyone for their warm wishes.”

The couple headed home with their daughter to join their son, Prince George, 21 months, who was in the care of his nanny, Maria Borrallo, before paying a visit to his sibling.

The toddler stole the show when arrived with his proud dad and gave a shy wave at the waiting crowds in a blue sweater that matched his father’s look.

Kate and William had presented their son on the very same steps after his birth on July 22, 2013.

Then, a visibly nervous Prince William cradled George in his arms, before admitting he had practiced fitting the baby seat into his Range Rover at home before the birth.

But it was a markedly different set of parents who confidently walked out with their newborn daughter on Saturday.

In a chivalrous gesture, William held his arm around his wife’s waist as if to steady her before they went back into the hospital for a few moments and then carried their daughter in a car seat to the vehicle.

The same medical team who delivered Prince George at the very same hospital on July 22, 2013.

The princess is the fourth in line of succession after Princes Charles, William and George.

Sources tell PEOPLE Kate and William and the children will stay at Kensington Palace for the next few days before heading to their estate in Norfolk.

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