The West Brom head coach was paid a bonus of a reported $3.78 million after he kept Palace in the Premier League at the end of the 2013-14 season.
Pulis had taken over at Selhurst Park with the club in the relegation zone, but after being paid the bonus for keeping them up as 11th-placed finishers he left before the start of the next season, on August 14 2014, after reported disagreements over player recruitment.
The Guardian reported Pulis was scheduled to receive the payment by the end of August 2014 and received it in advance after requesting it be brought forward.
Palace took the case to mediation under an independent tribunal, convened by the Premier League and brought under Football Association rules aimed at preventing disputes ending up in the courts.
The Premier League confirmed to Press Association Sport it convened the tribunal but had no further part in the case.
Sky Sports News reported the tribunal found in favour of Palace. There was no immediate response from Palace or West Brom to requests to confirm reports regarding the case.
The sum is reported to include a $1.89 million fine from the Premier League and the legal costs of both Pulis and Palace.
Neither party is allowed to comment on the case under the confidential terms of the arbitration, according to reports.