The Hungary international left the Potters for Italy four years ago after turning down the offer of a new contract.
Stoke have been fighting for recompense ever since, and their battle reached the Court of Arbitration for Sport earlier this year.
The Swiss court has now found in the Potters' favour, and chief executive Tony Scholes told the club website: "We are delighted with the outcome.
"This vindicates our persistence in pursuing Brescia for the compensation which we were clearly entitled to according to the rules set down by FIFA.
"We always considered that we had a very strong case and it was disappointing in many respects this matter could not have been resolved earlier."