The football club's appeal against FIFA's original ruling to award Falkirk around €250,000 in compensation was partially upheld by the Court of Arbitration for Sport, meaning City will now have to pay €65,000 less than first thought.
This news comes after Falkirk originally claimed for €330,000 in compensation following Stewart's move to the Coral Windows Stadium back in the summer of 2011.
The final confirmed compensation fee of €185,000 equates to just over £150,000.
The club can confirm to its supporters that this money has been accounted for in this season's budget.
Speaking to the club's Director of Operations David Baldwin, he said: "Clearly we are disappointed with this outcome as we felt there was no case to answer in this first place, hence why we appealed the original decision.
"We didn't feel any compensation was due.
"However, looking on the positive side of the outcome, we have seen a 25% reduction in the original judgement passed down by FIFA.
"From the club's perspective, despite our disappointment, we have to accept this appeal decision now and we move on."
In addition to today's appeal outcome, the club can reveal that it has already paid for all of costs that come with asking for a Court of Arbitration for Sport sitting.
As part of the appeal decision, however, the Court of Arbitration for Sport has ruled that Bradford City only pick up 80% of the court costs and Falkirk pay for the extra 20%. This means that 20% of the court costs for the appeal hearing will be due back to the club.