Stiles' former club paid £188,200 for the medal at an auction of football memorabilia in Edinburgh.
The price trumped the £165,000 fetched by Alan Ball's own World Cup medal five years ago.
Stiles, 68, made a total of £424,438 from his collection during today's sale.
Manchester United bought several of the 45 lots, which a representative from Convery Auctions said would be displayed in the club's museum.
Stiles said he had intended to leave the mementoes to his children, but decided to sell them after being unable to divide them up between his three sons.