Charles Green agreed to pay all football debt to clubs as part of a deal to have Rangers' member-ship of the SFA transferred to his new company in July 2012.
Despite reaching settlements with other European sides, Rapid remained unpaid as negotiations continued on how much was due from Rangers to the Austrian side.
According to Rangers' failed CVA in the summer, Rapid were owed £1million, but have settled for a payment of £715,000, which they have received.
Rapid are still pursuing the oldco, which is in liquidation, for the full £1m owed.
A spokesperson said: "We received the money from the new Rangers company on Tuesday to our bank and the matter with them is closed.
"We have assured them we will not raise any dispute with Fifa which could have potentially blocked their participation in future European competitions.
"We are still trying to recover the full amount from the old Rangers company, but we understand this may take many months."
The money was due as a third and final instalment for the transfer of the player in the summer of 2010.
It is understood GAIS, Orebro and Palermo have received negotiated amounts due for the transfers of Mervan Celik, Alejandro Bedoya and Dorin Goian respectively.