The new mom was all smiles as she waved from the car

Princess Eugenie and Jack Brooksbank are bringing their baby boy home.

The couple, who welcomed their first child on February 9, left The Portland Hospital in London on Friday as a family of three. 

The new mom was all smiles as she waved from the backseat of their car with her baby boy strapped in a car seat beside her as Jack was behind the wheel.

Eugenie and Jack will settle into life as new parents at Frogmore Cottage in Windsor. Eugenie's cousin, Prince Harry, and Meghan Markle lent their U.K. residence to the family of three.

The Portland Hospital is where Eugenie was born, as well as her older sister, Princess Beatrice. It's also where Meghan Markle gave birth to Archie, who will celebrate his second birthday in May.

Queen Elizabeth's granddaughter welcomed a son weighing 8 lbs., 1. oz. on Tuesday. This is the ninth great-grandchild for the monarch and Prince Philip and first grandchild for Eugenie's parents, Prince Andrew and Sarah Ferguson.

Princess Eugenie leaving Portland Hospital
Jack Brooksbank and Princess Eugenie
| Credit: Beretta/Sims/Shutterstock

The proud parents shared the first photo of their newborn on Instagram on Tuesday. The black-and-white shot shows their baby's hand wrapped around Eugenie's thumb while Jack holds the baby boy's arm. The new mom captioned the shot with blue heart emojis and two exclamation points to show her excitement.

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Predictions for what the parents will name their baby boy have been rolling in this week.

According to gambling site Betfair, Philip is the favorite in the betting odds for Eugenie and Jack to call their first child with 10/3 odds. The name would have special significance to the new mom as it's the name of her grandfather, Prince Philip, who will celebrate his 100th birthday in June.

Princess Eugenie leaving Portland Hospital
Princess Eugenie brings her baby boy home from the hospital on Feb. 12
| Credit: Beretta/Sims/Shutterstock

Ladbrokes also has traditional royal family names as the frontrunners: Arthur (a favorite in the betting odds since Eugenie announced her pregnancy in September) and Frederick are tied at the top (5/1), followed by James (6/1), Edward (8/1) and Albert (8/1).

Princess Eugenie and Jack
Jack Brooksbank and Princess Eugenie
| Credit: Princess Eugenie/Instagram

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Eugenie and Jack have been quietly enjoying married life since their lavish wedding at St. George's Chapel at Windsor Castle in October 2018.