On Wednesday, the 31-year-old princess pledged to look after “Granny”, the Queen, for Philip, who died on Friday aged 99.She also shared an image of herself with the Duke and her sister Princess Beatrice at the Epsom Derby in 2012, alongside one of Philip patting her on the head as a child after a Christmas Day church service.
“I remember learning how to cook, how to paint, what to read. I remember laughing at your jokes and asking about your spectacular life and service in the Navy," she wrote in an accompanying caption.
“I will remember you in your children, your grandchildren and great grandchildren.
"Thank you for your dedication and love for us all and especially Granny, who we will look after for you."
Eugenie's is the latest in a swathe of tributes to the Duke of Edinburgh from members of the Royal Family.
On Monday, Prince William and Prince Harry publicly honoured their grandfather.
In a statement, Prince William wrote: “I will miss my Grandpa, but I know he would want us to get on with the job.”
He also spoke of Philip's relationship with Kate and expressed his gratitude for the “kindness he showed her”.
Shortly after, his brother, Prince Harry, spoke of his grandfather, describing him as the "master of the barbecue".
The Duke of Sussex said his grandfather Prince Philip was “a man of service, honour and great humour, adding that “he was my grandpa: master of the barbecue, legend of banter, and cheeky right ‘til the end”.
Prince Philip's son, Prince Andrew refered to the Duke of Edinburgh as "the grandfather of our nation".
Prince Andrew added : "[The Queen] described it as having left a huge void in her life but we, the family, the ones that are close, are rallying round to make sure that we’re there to support her."
At the weekend, it was announced that the monarchy and their households would observe two weeks of royal mourning. However, members of the royal family will be “continuing to undertake engagements appropriate to the circumstances,” a royal official said.
Following this announcement, the Queen held her first in-person royal engagement since the death of her husband. The event, which took place on Tuesday, marked the retirement of her household’s most senior official Earl Peel, who had served as Lord Chamberlain.
Listen to the The Royal Rota on The Duke of Edinburgh's life, legacy and how he will be remembered: