Ross Baillie, 21, a finalist in the 110m hurdles at last year's Commonwealth Games, suffered the reaction after eating a chicken sandwich during a break in training in Bath on Wednesday.
Baillie, heralded as the natural successor to 110m hurdles world record holder Colin Jackson, was taken to the Royal United Hospital in Bath.
A spokeswoman for the hospital said: "Ross Baillie tragically died in the intensive care unit at 11am today. His family were at his bedside."
Baillie's parents, Hugh and Sheila, both former athletes, travelled from their home in Clydebank outside Glasgow on Wednesday evening to be with their son.
Sports Minister Tony Bank led tributes to the young athlete and called his death "an appalling tragedy".
"He was an immensely talented athlete with an extremely bright future ahead of him.
"Colin Jackson himself described Ross as his natural successor and that is no small compliment.
"My thoughts are with Ross's family - the enormous loss felt by British athletics is only a tiny fraction of what they must be feeling now."
The hurdler, who was in Bath preparing for the European junior championships in Finland, was with international swimmer Mark Foster when he collapsed.
They had both chosen a sandwich with a coronation chicken filling for their lunch but minutes after he bit into his sandwich, Baillie realised there were peanuts in it.
Mr Foster said: "As soon as he bit into it, Ross said he realised there were nuts in it and his tongue started swelling and he started to cough. The coughing continued so I put him in the car and took him to the nearest doctors as he was finding it increasingly difficult to breath.
He was quickly diagnosed by a doctor at the nearby University of Bath as suffering from a severe allergic reaction and given an adrenaline injection. But Baillie, a member of Glasgow's Victoria Park Athletic Club, never regained consciousness after being admitted.
A hospital spokeswoman said: "Staff in the Intensive Care Unit who cared for him over the last three days wish to extend their deepest sympathy to his family and friends."
Baillie broke the Scottish 110m hurdle record at the Commonwealth Games in Kuala Lumpur, Malaysia, and was tipped for gold in the junior championship this summer. He had been sharing a flat in Bath with Jackson who was helping to groom him for the future.
Jackson had tipped him to run under 13.20 seconds this year which would have put him among the world's best male hurdlers.
The 21-year-old ran for Britain at the World Indoor Championship in Japan in March this year and had twice broken the indoor 60m hurdles during the winter.
He was due to take part in an international meeting in Mannheim, Germany, this weekend as part of his preparation for the European junior championships in Finland.
Baillie's brother Chris, 18, is also a promising 110m hurdler and is tipped to follow in his footsteps.
Scottish Athletics Federation chief executive, David Joy, said that Baillie's death would be hard-felt by everyone who was involved in the sport.
He said: "The Scottish Athletics Federation are devastated by the news of the tragic death of Ross Baillie.
"Ross was a young man who was well-liked by everyone he met and had a lifetime of opportunity in front of him.
"The Baillie family is deeply involved in athletics and this news will stun the whole of the sports world.
"The Scottish Athletics Federation extends its sympathies to Hugh and Sheila Baillie and their family."
Ged Roddy, director of sport at the University of Bath, added his own tribute to Baillie, whose death has saddened his entire staff.
He said: "Ross Baillie was a talented young athlete and very popular with us all here. We are devastated by his loss and he will be greatly missed."
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