Winner of the 2001 Derby at Epsom, the horse was father to numerous champions including the legendary Frankel.
Owners Coolmore Stud announced he was put to sleep "on humane grounds owing to a chronic, non-responsive, debilitating injury to the left fore foot".
"It is a very sad day," said Coolmore owner John Magnier.
"We all feel incredibly fortunate to have had Galileo here at Coolmore.
"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."
The most successful Group One sire of all time has produced 91 individual Group One winners, while 20 of his sons have sired Group One winners on the Flat.
Galileo was the world's biggest stud - a stallion so valued that his breeding fee was not advertised, but thought to be well over £300,000 a time.
Reportedly worth more than £150m, he really was the Daddy.
As well as winning the Derby himself, he was the father of five subsequent winners of the famous Epsom race - New Approach, Australia, Ruler Of The World, Anthony Van Dyck and Serpentine.
His trainer Aidan O'Brien called him an "unbelievable" horse and said racing would probably never see such an "incredible story" again.
