"I will never take for granted the special memories my children will always have of their great-grandpa coming to collect them in his carriage," Prince William said

Prince William is honoring his beloved grandfather Prince Philip with a touching tribute in the wake of the Duke of Edinburgh's death on Friday.

On Monday, William shared a personal message and a never-before-seen family photo of his son Prince George with Prince Philip. The sweet photo, which shows the young prince reading a book as he sits beside his great-grandfather in his carriage, was taken by Kate Middleton in Norfolk in 2015.

Listen below to the episode of our daily podcast PEOPLE Every Day for continuing coverage in the wake of Prince Philip's passing.

Along with the photo, William said, "My grandfather's century of life was defined by service – to his country and Commonwealth, to his wife and Queen, and to our family.

I feel lucky to have not just had his example to guide me, but his enduring presence well into my own adult life – both through good times and the hardest days. I will always be grateful that my wife had so many years to get to know my grandfather and for the kindness he showed her. I will never take for granted the special memories my children will always have of their great-grandpa coming to collect them in his carriage and seeing for themselves his infectious sense of adventure as well as his mischievous sense of humour!

"My grandfather was an extraordinary man and part of an extraordinary generation. Catherine and I will continue to do what he would have wanted and will support The Queen in the years ahead. I will miss my Grandpa, but I know he would want us to get on with the job."

prince phillip, prince george
Prince Philip and Prince George in 2015
| Credit: The Duchess of Cambridge

William has previously said that his grandfather has been a role model throughout his life. In a 2018 speech at the Charity Commission Annual Public Meeting, Prince William praised Philip's work ethic.

"My father, of course, had inherited this very same habit from his parents," he told the crowd. "My grandfather Prince Philip has been one of the most tireless public servants of this country, deeply committed to helping young people fulfill their potential."

Prince Philip, Prince William
Prince Philip and Prince William
| Credit: Chris Jackson/WPA Pool/Getty

William also admired how Prince Philip supported Queen Elizabeth in her role as monarch.

"She regularly talks in private about how much he's been a support to her," William said of his grandparents in the documentary Elizabeth at 90: A Family Tribute. "He's totally put his own personal career aside to support her. And he never takes the limelight, never oversteps the mark. He's always on her side, he's an unwavering companion."

Prince Philip, Will, Kate
Prince Philip, Prince William and Kate Middleton
| Credit: Max Mumby/Indigo/Getty

Kate also looked to Philip in how he supported the Queen, as she will someday be consort to Prince William when he is king.

"To be able to do that by yourself I think would be a very lonely place to be, but I think to have the support of your husband there by your side on those occasions and behind closed doors as well I think is really special," Kate said in the documentary.

Kate Middleton, Prince Philip
Kate Middleton and Prince Philip
| Credit: Samir Hussein/WireImage

Prince Philip — who retired from his public duties in August 2017 — died at age 99. He is survived by his wife of 73 years, Queen Elizabeth, their daughter Princess Anne and their three sons: next-in-line-to-the-throne Prince CharlesPrince Andrew and Prince Edward. He also leaves behind eight grandchildren, including Prince William and Prince Harry, and nine great-grandchildren, including Prince GeorgePrincess Charlotte, Prince LouisArchie and Princess Eugenie's son August, whose middle name was Philip after his great-grandfather.

Prince Philip, Will, Kate
Prince Philip, Prince William and Kate Middleton
| Credit: Samir Hussein/WireImage

The Duke of Edinburgh was hospitalized on Feb. 16 after being taken to King Edward VII hospital in London on the advice of his doctor after "feeling unwell," Buckingham Palace said in a previous statement.

He left Windsor Castle — where he had been staying with the Queen since November amid the latest COVID-19 lockdown in the U.K. — in the evening and was expected to remain in the hospital for a few days. Palace sources stressed that it was not an emergency admission and that Philip walked into the hospital unaided. The illness was later revealed to be an infection.

During an outing on Feb. 22, Prince William gave a short health update on his grandfather, saying, "He's okay. They're keeping an eye on him."

Philip "passed away peacefully" on Friday at Windsor Castle. Royal officials said Philip's funeral service will take place April 17, as expected, and his coffin will be processed through Windsor Castle.

The funeral will be at St. George's Chapel at Windsor Castle at 3 p.m. U.K. time (10 a.m. ET) and will be broadcast live. The first details were confirmed at a briefing held by palace officials on Saturday.

Can't get enough of PEOPLE's Royals coverage? Sign up for our free Royals newsletter to get the latest updates on Kate Middleton, Meghan Markle and more! 

It will be known as a ceremonial royal funeral and not a state funeral, which are generally reserved for monarchs. The funeral plans take into account the country's COVID guidelines and is "much reduced in scale with no public access," a palace spokesman said.

The funeral will take place entirely within the grounds of the castle and plans have been given final approval by the Queen but they "still very much reflect the personal wishes of the Duke. The occasion will still celebrate and recognize the Duke's life and his more than 70 years of service to the Queen, the U.K. and the Commonwealth."

On the day of the funeral, at around 2:40 p.m in the U.K. (9:40 a.m. ET) on April 17, Philip's coffin will be moved in a small ceremonial procession from the state entrance to the castle to the chapel. The funeral will begin with a nationally-observed minute's silence at 10 a.m. (3 p.m. U.K. time).