Video report by ITV News Royal Editor Chris Ship
In a tribute to his grandfather, Prince William wrote: “I will miss my Grandpa, but I know he would want us to get on with the job.”
William is the first of Philip’s grandchildren to publicly honour his memory and in a statement spoke of his relationship with Kate and expressed his gratitude for the “kindness he showed her”.
Shortly after, his brother, Prince Harry, also 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”.
In a statement, William says: “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.”
Kensington Palace shared a touching new photograph taken by the Duchess of Cambridge of a young Prince George with his great-grandfather Philip alongside the message from William.
George, a future king, is pictured sat beside the duke on the box seat of a carriage, as Philip held the reins and a whip.
George, dressed in shorts and a knitted jumper, is holding open a picture book.
The image was taken in Norfolk in 2015.
The palace confirmed on Saturday the duke would be flying back to the UK, but the Duchess of Sussex, who is heavily pregnant with the couple's second child, has been advised by doctors against flying.
In a statement issued through his foundation Archewell, Harry said: “My grandfather was a man of service, honour and great humour. He was authentically himself, with a seriously sharp wit, and could hold the attention of any room due to his charm—and also because you never knew what he might say next.
“He will be remembered as the longest reigning consort to the Monarch, a decorated serviceman, a Prince and a Duke. But to me, like many of you who have lost a loved one or grandparent over the pain of this past year, he was my grandpa: master of the barbecue, legend of banter, and cheeky right ‘til the end.
“He has been a rock for Her Majesty The Queen with unparalleled devotion, by her side for 73 years of marriage, and while I could go on, I know that right now he would say to all of us, beer in hand, ‘Oh do get on with it!’
“So, on that note, Grandpa, thank you for your service, your dedication to Granny, and for always being yourself. You will be sorely missed, but always remembered—by the nation and the world. Meghan, Archie, and I (as well as your future great-granddaughter) will always hold a special place for you in our hearts.
“‘Per Mare, Per Terram.’”
Over the weekend the duke’s four children spoke movingly about the loss of their father and how the Queen is stoically coping after her husband of 73 years died peacefully on Friday.
William's father, Prince Charles, had spoken warmly of his “dear papa” on Saturday, describing him as having “given the most remarkable, devoted service to the Queen, to my family and to the country, but also to the whole of the Commonwealth”.
After a church service on Sunday, Prince Andrew revealed his mother's feelings: “She 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.”
Prince Andrew said his mother is “an incredibly stoic person”, with his sister-in-law the Countess of Wessex adding that the Queen is “thinking of others before herself”.
The Earl of Wessex said his mother is “bearing up” and that the “wave of affection” for his father and “fantastic” tributes are appreciated by the family.
Andrew described the death of his father as resonating with many people, saying: “We’ve lost almost the grandfather of the nation.”
In a message released later on Sunday, the Princess Royal added her thanks to the public, as she paid tribute to her father as someone who “leaves a legacy which can inspire us all”.
Anne said: “My father has been my teacher, my supporter and my critic, but mostly it is his example of a life well lived and service freely given that I most wanted to emulate.”