"Thank you for the birthday love yesterday...I got the best present I could ask for!" Princess Eugenie wrote on Instagram

Princess Eugenie is all aglow as she settles into new motherhood with her son August.

On Wednesday, the royal, who celebrated her 31st birthday on Tuesday, shared two sweet new photos on Instagram of her and husband Jack Brooksbank with their baby boy, who was born on Feb. 9.

"Thank you for the birthday love yesterday❤️.. I got the best present I could ask for!!" she captioned the photo, which shows Eugenie and Jack smiling at one another as the proud new mom royal cradles their son.

The six-week-old newborn is cozy in a white knit sweater that's embroidered with his name in blue. In a second photo, August looks straight into the camera as he snuggles into his dad's shoulder.

Eugenie and Jack named their son August Philip Hawke. In choosing their son's middle name, the couple honored Eugenie's grandfather, Prince Philip, who recently returned home to Windsor Castle after a month-long stay in the hospital.

Princess Eugenie
Jack Brooksbank, Princess Eugenie and son August
| Credit: Princess Eugenie/Instagram
princess eugenie
Jack Brooksbank and baby August
| Credit: princess eugenie/instagram

Eugenie and Jack are now settling into life as a family of three near her grandparents at Frogmore Cottage — the Windsor home of Prince Harry and Meghan Markle. The Sussexes lent Eugenie their home, which is close to Windsor Castle, where Queen Elizabeth and Philip have been staying amid the pandemic.

The Queen celebrated her granddaughter's birthday on Tuesday with a special message on social media.

"Wishing Princess Eugenie a very happy birthday today!" the captioned read along with the birthday cake and red balloon emoji.

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Soon after August's birth, Eugenie introduced her baby boy to the world with a relatable social media post that featured photos taken in the couple's backyard.

Princess Eugenie
Jack Brooksbank, Princess Eugenie and their son August
| Credit: Princess Eugenie Instagram

"We wanted to introduce you to August Philip Hawke Brooksbank," Eugenie wrote. "Thank you for so many wonderful messages. Our hearts are full of love for this little human, words can't express. We are excited to be able to share these photos with you."

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A source recently told PEOPLE that Eugenie is "doing really well" after having a C-section due to her previous spinal surgery for scoliosis.

The source added that Eugenie "sounded very content and said the baby is a complete dream!"