The sire of Frankel and so many other great champions, the Aidan O'Brien-trained son of Sadler's Wells was a brilliant racehorse in his own right.
His finest hour came at Epsom in the 2001 Derby, before he followed up in the Irish Derby and the King George VI And Queen Elizabeth Stakes.
Coolmore said in a statement on Saturday: "Regretfully our world-renowned Champion Sire Galileo was put to sleep earlier today on humane grounds owing to a chronic, non-responsive, debilitating injury to the left fore foot."
John Magnier paid tribute to a horse that leaves a "lasting legacy".
He said: "It is a very sad day, but we all feel incredibly fortunate to have had Galileo here at Coolmore.
"I would like to thank the dedicated people who looked after him so well all along the way. He was always a very special horse to us and he was the first Derby winner we had in Ballydoyle in the post M V O'Brien era.
"I would also like to thank Aidan and his team for the brilliant job they did with him. The effect he is having on the breed through his sons and daughters will be a lasting legacy, and his phenomenal success really is unprecedented."
Out of the Arc-winning mare Urban Sea, Galileo won his first six starts and headed to Epsom off the back of victories in the Ballysax Stakes and Derrinstown Stud Derby Trial - now known as the 'Galileo route'.
Ridden by Mick Kinane in the premier Classic, he was sent on his way as the 11-4 joint-favourite with Golan and beat Sir Michael Stoute's runner by three and a half lengths.
The Curragh and a four-length victory over Morshdi was next, before Ascot and the King George saw a two-length triumph from Fantastic Light.
The pair met again in the Irish Champion Stakes, when this time Fantastic Light and Frankie Dettori came out on top after an epic battle.
Galileo finished his racing career in the Breeders' Cup when sixth to Tiznow on the dirt at Belmont Park.
He was the sire of five Derby winners - New Approach, Australia, Ruler Of The World, Anthony Van Dyck and Serpentine - and has a total of 91 individual Group One victors. Remarkably, 20 of his sons have also sired Group One winners.
He will be forever associated with Frankel, who was unbeaten throughout his career for Sir Henry Cecil.
O'Brien spoke of his pride at having trained Galileo, and then so many of his progeny.
He told the PA news agency: "He was an unbelievable horse for everybody involved with him. What he did was exceptional.
"John did an incredible job managing him and recognised the mares that were going to suit him.
"He recognised how good he was very young, and he was always so highly thought of before he even came to Ballydoyle.
"He was our first Derby winner from Ballydoyle, and we were so fortunate to have him.
"It's an incredible story, and obviously we'll probably never see it ever again.
"What made him very special was the attitude that he put into his stock. We'd never seen anything like that.
"He was a massive horse physically. But the tremendous determination and genuineness he put into all his stock was unique really."
Looking back on his racing career, O'Brien said: "It was unreal - he won his maiden, the two trials and then the Derby, Irish Derby and King George.
"He looked different as well going through his races - he didn't look like any other thoroughbred. He had loads of genuine power.
"His stock had that as well - and the determination to put their heads out the same way he galloped.
"He'll be sorely missed by us all."