The move was announced following consultations between the two clubs earlier this week and follows the late postponement of the original match between the sides last month after a torrential downpour flooded a previously playable pitch.
A statement issued by Hearts said: “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.
“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.”