Denman, the 2008 Cheltenham Gold Cup winner, died on Tuesday at the age of 18, trainer Paul Nicholls announced.
Nicholls said the brilliant chaser "had begun to go downhill in the past few days", and was "put to sleep painlessly".
The Ditcheat handler said: "The decision was taken by his devoted owner Paul Barber with the full support of myself, our head lad Clifford Baker and our vet Buffy Shirley-Beavan.
"We all agreed it was the right thing to do because he had begun to go downhill in the past few days and we did not want to see him suffer."
Denman was renowned for his iron will on a racecourse and won 14 races from 24 starts.
His finest hour came in the 2008 Cheltenham Gold Cup, when he defeated stablemate Kauto Star by seven lengths in a race for the ages.
Denman claimed four Grade One races and was also twice successful in the Hennessy Gold Cup at Newbury in 2007 and 2009. He retired in 2011 and earned over £1million in prize-money.
Nicholls said on the Betfair website: "Denman was known affectionately to punters and racegoers as 'The Tank', which I always felt was a fitting description.
"He was a magic horse who had a tremendous following because of the wholehearted way he went about his racing.
"He was tough, hardy and willing, wasn't the easiest to train, and would bite your hand off in his box given half a chance.
"He came along at the right time and was one of our superstars during a golden era for Team Ditcheat."
Denman initially took up team chasing with Charlotte Alexander following his retirement. before returning to Ditcheat where he was cared for by owner Paul Barber's daughter-in-law Emma.
Nicholls described Barber as "immensely proud of Denman's achievements on the racecourse" and recounted how the gelding came to join his team.
He said: "I remember seeing Denman for the first time at Adrian Maguire's yard near Cork while Paul and I were on a shopping trip in Ireland. It was a few weeks after he had won his maiden point-to-point in March 2005. I was bowled over by Denman's presence and raw power as he was led into view.
"He had only taken a few steps when I told Adrian I'd have him. The words were hardly out of my mouth when Paul Barber countered, 'No you won't. I'm having him'. Neither of us had any cause to regret the deal that took Denman home to Ditcheat."
Denman was diagnosed with a fibrillating heart in the autumn following his Gold Cup win and Nicholls felt he lost a little of his brilliance after that problem.
He added: "Denman took a long time to recover his condition and full strength once back in training and in my view was never quite as good again.
"But he showed that he still retained his competitive edge and plenty of ability by winning a second Hennessy Gold Cup with an astonishing performance under top weight and also finishing runner up in three more Gold Cups.
"When he retired in 2011 he had earned in excess of £1million with 14 victories from 24 starts under rules, but mere statistics cannot possibly do him justice."
Walsh spellbound by second Hennessy
Ruby Walsh pinpointed Denman's 2009 Hennessy Gold Cup as the best performance of his career.
While Denman famously topped fellow Paul Nicholls inmate Kauto Star in a spectacular face-off in the 2008 Cheltenham Gold Cup, Walsh believes his Newbury win the following year was the standout moment of his 24-race career.
Walsh was in the plate that day as Denman dished out a three-and-a-half-length beating to stablemate and subsequent dual Grade One winner What A Friend, to whom he was conceding 22lb.
He told Paddy Power News: "He was an incredible athlete and his second Hennessy Gold Cup win in 2009 was the best weight-carrying performance by a horse that I've ever been involved in.
"He was probably a handicap certainty when he won his first Hennessy off a mark of 161, but to win his second off a mark of 174, which was 13lb higher than when he won it the first time, that was incredible.
"As good as his Gold Cup win was, what he did in that second Hennessy Gold Cup, off that mark, was amazing.
"To give What A Friend 22lb, who won a Lexus and a Betfair Bowl on his next two starts, was just incredible. To me, that was his greatest ever performance."
Sam Thomas partnered Denman to his Gold Cup success, with Walsh riding Kauto Star, and admits he was not surprised to see his mount turned over on that occasion.
He said: "I wasn't surprised that Denman beat Kauto that day. They were two phenomenal horses to come along at the same time and they had a great rivalry.
"What Denman did in that year's Gold Cup was unbelievable and the gallop he went was incredible. To have so many horses beaten so early that day was unbelievable. He was a wonderful horse."
Walsh rode Denman 10 times, winning three Grade Ones, including the 2007 Lexus Chase.
He added: "For such a big horse, he had such movement of his feet in front of a jump - it was incredible.
"He was a brilliant horse to ride over a fence and he was just an unbelievable athlete. He had a brilliant career and he was a very good novice hurdler but chasing was always going to be his forte.
"He excelled over fences. He was unbeaten as a novice over fences and he went unbeaten for a long time over fences. He bolted up in the RSA and his performance in the Hennessy with Sam Thomas was spectacular.
"He was just an incredible racehorse and an incredible athlete."