The two sides will meet at Tynecastle in a rearranged Ladbrokes Premiership fixture after the initial match was postponed due to a waterlogged pitch.
Travelling fans criticised Hearts after the official club Twitter feed announced two hours prior to the postponement that no pitch inspection was planned and the match would go ahead.
Hearts hope the goodwill gesture will help make up for the prior inconvenience to some fans.
A statement on the website read: “Hearts is pleased to confirm that, following discussions last week and careful deliberation, we will cover the cost of the official Partick Thistle supporters’ buses to travel through to the capital this weekend.
“As we all know, the previously postponed game was called off just before 1pm on Saturday 13th February following persistent heavy rain and then a late torrential downpour which effectively flooded parts of what had been a playable pitch.
“This caused considerable inconvenience and cost to many supporters from both clubs. While we cannot reimburse every individual supporter on a case by case basis, we hope that this gesture will demonstrate the club’s appreciation of just how difficult things can be for supporters.
“We felt it was particularly relevant given the fine gesture from Partick Thistle during season 2013/14 when Hearts were in administration and a donation was made by the Maryhill club in relation to travelling Gorgie fans.”
THE SCOTSMAN ON SOCIAL MEDIA