Denman, the 2008 Cheltenham Gold Cup winner, died on Tuesday at the age of 18, trainer Paul Nicholls told Betfair.
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: "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."
Dan Skelton was assistant trainer to Nicholls during Denman's career and was fulsome in his praise for Denman's attitude.
He tweeted: "Don't (mind) admitting I thought Kauto would win the 2008 GC (Gold Cup). What Denman did was incredible and was a performance for the ages. He was obviously super talented, but I loved that rugged ambition to win at any cost.
"A sad day, that feels like the end of an era. These two were a fixture of my Racing education and to be fair it now seems surreal to have been a little part of it and to have been able to witness their careers. How lucky were we all!"
Cheltenham and Newbury hosted the highlights of Denman's career and both tracks were keen to pay tribute on social media.
A tweet issued by Cheltenham read: "A true hero and Gold Cup legend. Rest easy Denman, and thank you for the memories."
Newbury added on Twitter: "An incredible achievement that will never be forgotten. Denman is forever ingrained in our history and his passing is felt by all at Newbury Racecourse. Seven races here, five wins, two Hennessy Gold Cups - a legend of Newbury and a legend of the sport of horse racing #RIPDenman."