The couple's little boy arrived on 9 February at 8.55am at London's Portland Hospital, weighing 8lbs 1oz, and husband Jack was at Eugenie's side for the happy moment.
Now everyone's wondering what the daughter of Prince Andrew and Sarah Ferguson will name her baby. Duchess Kate and Duchess Meghan took around two days to reveal the names of their newborns so Friday could be the day.
WATCH: Princess Eugenie welcomes baby boy!
Will Princess Eugenie choose a traditional name, perhaps paying homage to another royal man, or will the new mother opt for a more modern moniker as her cousin Prince Harry did with his son Archie Harrison?
Online bookies had tipped Eugenie and Jack to name their son Arthur, but odds changed overnight on Wednesday with Betfair putting the moniker Philip as the new favourite into 10/3 from 25/1 after a flurry of bets. Oliver has also become the second favourite at 4/1.
The Princess has an incredible relationship with her grandfather Philip, who she affectionally calls "Grandpa," and it would be a beautiful tribute to him to name their son after him.
Eugenie has spent a lot of time with her grandparents and is also very close to the Queen - who is said to have a special bond with her sixth-born grandchild. The new mother refers to the monarch as "Granny" and before COVID-19 restrictions, she was a regular visitor to their Scottish estate in Balmoral.
"Family-wise we’re all there, so it’s a lovely base for Granny and Grandpa to be. For us to come and see them up there, where you have room to breathe and run," she said of Balmoral in the documentary, Our Queen at Ninety.
Eugenie shared this first photo of her son on Tuesday
Her Majesty the Queen is usually one of the first people to know about the birth of a royal baby and typically approves the names of those closest in line to the throne.
While Eugenie is Her Royal Highness Princess Eugenie of York, it doesn't automatically mean that her son will also inherit a title.
As things currently stand, the royal baby will not have a title because these are passed down the male line and Jack does not have a title.
However, the Queen could decide to intervene and give Eugenie's husband an earldom or issue a Letters Patent amending the rules.
The tot will be known as Master Brooksbank, like Prince Harry and Meghan's son is styled as Master Archie Harrison Mountbatten-Windsor.
Princess Eugenie as a newborn outside The Portland Hospital in London
The official birth announcement
Buckingham Palace announced the royal baby's birth on Tuesday in a statement that read: "Her Royal Highness Princess Eugenie was safely delivered of a son today, 9th February 2021, at 0855hrs at The Portland Hospital. Jack Brooksbank was present. The baby weighs 8lbs 1oz."
The statement continued: "The Queen, The Duke of Edinburgh, The Duke of York, Sarah, Duchess of York, and Mr and Mrs George Brooksbank have been informed and are delighted with the news.
"This is Princess Eugenie and Jack Brooksbank's first child, The Duke of York and Sarah, Duchess of York's first grandchild, and the ninth great-grandchild for The Queen and The Duke of Edinburgh. Her Royal Highness and her child are both doing well."
Princess Eugenie and Jack Brooksbank announced their pregnancy in September
When it comes to picking baby names, the royals like to keep things traditional and often choose one that pays homage to another family member or a past ancestor.
Eugenie's own name – Eugenie Victoria Helena – has a very special meaning behind it. She was named after Victoria Eugenie of Battenberg, the granddaughter of Queen Victoria and the daughter of Princess Beatrice of the United Kingdom.
Her middle name Helena is a tribute to Princess Helena of the United Kingdom, who was the fifth child and third daughter of Queen Victoria and Prince Albert.
Meanwhile, Jack's full name is Jack Christopher Stamp Brooksbank.
The new royal baby is 11th-in-line to the throne behind mum Eugenie and he is also the Queen's ninth great-grandchild.
Eugenie and Jack married in October 2018
Where do Princess Eugenie and Jack Brooksbank live?
Eugenie and Jack are raising their new baby boy at Frogmore Cottage in Windsor, after Prince Harry and Meghan Markle allowed them use of the property while they are in the USA, in order to accommodate their growing family.
"Eugenie and Harry have always been close and they chat privately all the time," a friend previously told HELLO! after the couple moved into the house in November 2020.
"It was Harry who suggested she and Jack could use Frogmore Cottage because it is much bigger than their cottage at Kensington Palace. It is a case of one family member reaching out to another."
The royal baby's first photo
Eugenie broke a new record when she shared the first glimpse of her baby son on her personal Instagram account on Tuesday.
The black and white shot, which showed the proud parents holding their newborn's tiny fingers, is now her most liked post with over 497,000 likes.
When will the royal baby be christened?
The royals at Eugenie's christening in 1990
A royal baby is also usually christened in a private baptism around three or four months after his or her birth, but this is one tradition Eugenie could decide to break.
Princess Eugenie was baptised at St Mary Magdalene Church in Sandringham in December 1990 and she was the first royal baby to have a public christening.
Prince Andrew and Sarah decided to give their youngest daughter a public baptism during the regular Sunday church service.
While the media and members of the public have gathered outside churches to see royal christenings in recent years, the ceremony has taken place behind closed doors.
Godparents chosen by the parents are usually royal cousins and relatives, as well as family friends.
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