The new parents of a baby girl phoned relatives, including Prince Harry and Queen Elizabeth

By Simon Perry
Updated May 02, 2015 08:25 AM

Amid the chaos and hubbub outside London’s St. Mary’s Hospital, inside, Princess Kate and Prince William were spending the first few magical hours alone with their newborn daughter.

Although most new parents don’t have the world’s media camped outside their doorstep, just like any other excited new mom and dad, the couple immediately called their loved ones to break the good news.

Indeed, a source told PEOPLE the couple spent the two and half hours between their little girl’s birth and the announcement of her safe arrival on the phone to family and friends.

Prince Harry, 30, was called halfway across the world, where he is currently on secondment to the Australian army.

A royal source told PEOPLE: “The good thing about the baby being born in the morning means Harry was still up.”

Harry made a brief trip home a week ago – and narrowly missed the birth of his new niece.

Meanwhile, great-grandmother Queen Elizabeth was told the news mid-morning before she joined her son Prince Andrew for an engagement at Richmond Castle in Yorkshire, and delighted grandpa Prince Charles, 66 – who publicly declared this week he was hoping for a granddaughter – was phoned at his country home, Highgrove.

Carole and Michael Middleton are not believed to be at Kensington Palace, where Prince George, 21 months, is being cared for by his nanny Maria Borrallo.

As for William’s uncle, Charles Spencer, he sent out his own congratulations via Twitter.

With sources saying Kate and William could leave the hospital as early as Saturday afternoon, the royal couple must be keen to introduce Prince George to his little sister.

Royal Baby Arrives: Kate Gives Birth to a Baby Girl