The 20-time champion jockey rode the Henrietta Knight-trained gelding to five of his 25 career victories, most notably his thrilling triumph over Direct Route in an unforgettable renewal of the Queen Mother Champion Chase at Cheltenham in 2000.
McCoy recalls how he first got the ride on Edredon Bleu two years earlier.
He told Press Association Sport: "I remember Richard Dunwoody rode him one day at Ayr and didn't think he was the nicest ride. Jim Culloty obviously rode him after that, and I was lucky to get on him at Sandown one day when Jim got injured.
"I got off him at Sandown and told Hen he was a certainty for the Grand Annual at Cheltenham. She said if I thought that then I could ride him.
"I remember ringing Martin Pipe to ask him if he could either not run anything in the race or let me off to ride him, and he said I could.
"I knew he was a certainty going into the race. I just couldn't see how anything could beat him in a handicap over two miles.
"The only thing that might have got him beat was me going too quick on him - I think I was 10 lengths clear at the water jump - but thankfully he was so well handicapped it didn't matter."
Edredon Bleu went on to finish second in the following year's Champion Chase, before going one better 12 months later in a race for the ages.
McCoy added: "It's different now, because the fence is no longer there, but I always said coming down to that second-last fence in a Champion Chase was as big a thrill as you could get riding. You went down to it so fast and you needed to be so accurate at it.
"Edredon Bleu wasn't visually brilliant to look at, but he was so fast, quick and accurate at his fences and got away from them very quickly.
"He gave me my only win in the Champion Chase, so I'll always be grateful to him for that."
