He passed away peacefully at home early on Saturday morning, his wife Mercedes Baker confirmed to The New York Times.
Whittington grabbed national attention in 2006 when Mr Cheney shot him in a dramatic hunting accident.
The accidental shooting unfolded on 11 February 2006 – midway through Mr Cheney’s second term as vice president to President George W Bush – when the two men were among a group hunting quail on a south Texas ranch.
When a group of birds took flight, Mr Cheney had wheeled around and taken a shot, accidentally shooting Whittington in the face and torso.
Whittington, who was 78 at the time, was rushed to hospital with multiple gunshot wounds.
At the time, it was said that he had suffered a minor heart attack caused by bullet fragments hitting blood vessels close to his heart.
Years later, Whittington revealed that his injuries were more serious than was publicly revealed.
Shockingly, the victim was blamed by the White House and eyewitnesses for what happened, claiming he stepped in Mr Cheney’s line of fire.
And, more bizarrely still, Whittington issued a public apology to the vice president – while recovering from multiple injuries.
“We all assume certain risks in whatever we do, whatever activities we pursue. And regardless of how experienced, careful and dedicated we are, accidents do and will happen,” he famously said on leaving hospital.
“My family and I are deeply sorry for all that Vice-President Cheney and his family have had to go through this past week.
“We send our love and respect to them, as they deal with situations that are much more serious than what we’ve had to deal with this week.”
He added: “We hope that he will continue to come to Texas and seek the relaxation that he deserves.”
It remains unclear whether or not Mr Cheney returned his apology, publicly saying at the time: “Thankfully Harry Whittington is on the mend and doing well.”
In his 2011 memoir In My Time, the former vice president described the incident as one of the “saddest” days of his life and said he was “of course, deeply sorry”.
“I, of course, was deeply sorry for what Harry and his family had gone through,” he wrote.
“The day of the hunting accident was one of the saddest of my life.”
Mr Whittington rarely hunted after the accident and reportedly kept his bloodied vest to teach his children the dangers of guns, according to The Washington Post.
Outside of the hunting accident, Whittington was a prominent Texas attorney who was well-known in the state’s Republican circles.
Born into a family of Democrats in Henderson, Texas, in 1927, Whittington became one of a key group who switched to Republican and built the party’s prominence in the state.
After studying law at the University of Texas, he joined George H.W. Bush’s 1964 unsuccessful campaign for the US Senate and was a donor for the younger Bush’s two successful presidential elections.
He was also elected to several Texas boards including the Texas Department of Corrections and the Texas Board of Criminal Justice.
In 2001, he called on then-Governor Rick Perry to ban the execution of developmentally disabled prisoners. Mr Perry refused but the Supreme Court banned the practice some time later.
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