The Duke of Cambridge described Philip as an "extraordinary man" while the Duke of Sussex said he was "a rock for Her Majesty the Queen with unparalleled devotion".
The royal brothers are the first of Philip's grandchildren to publicly honour his memory, and Harry light-heartedly summed him up as "master of the barbecue, legend of banter, and cheeky right till the end".
William spoke candidly about Philip's relationship with Kate and expressed his gratitude for the "kindness he showed her".
He also highlighted the special bond between the duke and Prince George, Princess Charlotte and Prince Louis, who would have "special memories" of being picked up in a horse-drawn carriage by their "great-grandpa".
William pledged to uphold his grandfather's wishes and continue, along with wife Kate, to support the Queen and "get on with the job".
Over the weekend Philip's four children spoke movingly about the loss of their father and how the Queen was being very "stoic" after losing her husband of 73 years who died peacefully on Friday.
"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."
Philip and the Queen provided a safe haven for William and Harry in the days following the death of their mother Diana, Princess of Wales, as they grieved at their grandmother's royal residence, Balmoral in Scotland, in 1997.
It is said Philip later suggested William and Harry walk behind their mother's coffin with him and other senior royals as the funeral cortege made its way through the streets of London.
William added: "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."
Kensington Palace tweeted William's statement with a touching photograph taken in 2015 of a two-year-old George with his great-grandfather Philip.
William concluded: "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."
Harry and William are expected to join their father the Prince of Wales and other senior royals in walking behind their grandfather's coffin as the funeral procession makes its way through Windsor Castle.
Philip's funeral might give the royal brothers the time and space to begin healing their rift which Harry spoke about during his Oprah Winfrey interview, and also to repair his relationship with father Charles.
Harry said in his tribute: "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."
Philip was famed for his quips, gaffes and outspoken comments that regularly made newspaper headlines during the decades he carried out his royal duties.
He once declared "British women can't cook", described plans for the Duke and Duchess of York's house at Sunninghill Park as looking "like a tart's bedroom", and asked Sir Tom Jones after the 1969 Royal Variety Performance: "What do you gargle with - pebbles?"
"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!'"
Harry ended by thanking his "Grandpa" for "your service, your dedication to Granny, and for always being yourself", and said he and his family - wife Meghan, son Archie and their unborn daughter - would always hold a "special place for you in our hearts".
Philip was Captain General of the Royal Marines for 64 years before retiring in 2017 and Harry briefly succeeded him before stepping down as a working royal last year and moving with Meghan to America.
As a parting message Harry quoted the motto of the Royal Marines: "Per Mare, Per Terram" - Latin for "By Sea, By Land".
Harry is quarantining ahead of Saturday's funeral at his former home of Frogmore Cottage in the grounds of Windsor Castle, after arriving in the UK over the weekend without his pregnant wife who was advised not to travel.