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.
Denman wins the 2008 Cheltenham Gold Cup
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.”