Bryn Parry passed away on Wednesday at the age of 67, the charity said.
Mr Parry and his wife Emma founded Help for Heroes in 2007 after learning about ex-servicemen's struggles to access rehabilitation treatment.
Prince William described him as "a life-affirming and inspirational man".
In a tweet, the prince said he was "deeply sad to hear that Bryn Parry has passed away".
"A life-affirming, inspirational man, his work with @HelpforHeroes made a difference to so many and his legacy will be its continuing impact."
Prince Harry also expressed his condolences in a statement published on his own veteran's charity, the Invictus Games Foundation.
"Today is a truly sad day for the military community as we bid farewell to a man who, alongside his wife, completely transformed the UK charity sector for the benefit of those that have served," he wrote.
"His vision, determination and brilliance provided a lifeline for thousands of veterans, as well as their families, when they needed it most."
The minister for veterans' affairs, Johnny Mercer, also paid tribute, saying Mr and Mrs Parry had "revolutionised veterans' care in the UK".
The MP for Plymouth, Moor View, added: "(Mr Parry) inspired me with his unapologetic determination to do the right thing by these men and women who serve.
"He will never be forgotten."
Mr Parry, who forged a career as a cartoonist after leaving the Royal Green Jackets, initially set out to raise £10,000 for wounded veterans with his wife through a charity cycle ride.
Within three years the couple, who are from the village of Downton near Salisbury, had raised £50m.
The charity's chief executive James Needham said: "Without Bryn, this charity wouldn't be here. Without him, over 27,000 veterans and their families wouldn't have received life-changing support.
"Bryn was instrumental in changing the focus of the nation and the way we regard both military service and wounded veterans."
He added: "Bryn's founding principles and his no-nonsense approach of doing everything humanly possible to help our heroes, remain at the heart of all we do."
Speaking to the BBC in 2010, Mr Parry said he and his wife felt there had been a lot of pent up public support for veterans that had no outlet.
"The problem was, people were concerned about the politics and the rights and wrongs of the wars," he said.
"We said it's not about the rights and wrongs of war, it's about a 22-year-old boy who's had his legs blown off.
"That allowed people to get behind the movement. It's just been a humanitarian desire to do something, and not stand around and feel helpless."
Mr Parry's cartoon business, Bryn Parry Studios, announced earlier this year that he had been diagnosed with stage four pancreatic cancer and would not be taking on any new commissions.
In a statement on its website, it said: "He is comfortable at home, surrounded by his family and mad dogs!"