The company has not specified the purchase price.
The purchase from Crushing Services International, a subsidiary of mining services company Mineral Resources, follows a move by FMG in September to take control of Christmas Creek's processing facilities due to operational concerns after an onsite death.
Christmas Creek has been rattled by two deaths in recent months, with contractor Kurt Williams killed in a crushing incident last August and Allen Zuvela killed in an incident at a heavy vehicle workshop in late December.
Sale of the facilities transfers full ownership and operational responsibility to FMG.
The miner has worked closely with CSI since it exercised its step-in rights to ensure a safe and hazard-free operation.
FMG has since employed 121 members of CSI's workforce.
FMG chief executive Nev Power thanked the management and owners of CSI for their cooperative approach during the step-in and the buy-out negotiations.
"This cooperative approach has ensured a smooth transition throughout," Power said.
"This outcome will assist in ensuring cultural alignment amongst the valued personnel who are responsible for the day to day operation of these important assets."
The buy-out of the finance lease for the facilities was also flagged as a continuation of FMG's ongoing debt reduction program.
"Fortescue sees this acquisition as an extremely positive benefit for the continued growth of the company." Power said.
"We are now getting substantial volume and revenue increases from our expanded operations, which are generating significant free cash flow and underpinning our accelerated debt reduction program."
The company began its debt reduction program in the September quarter with the voluntary redemption of $A140 million in preference shares.
Its net debt position as of September 30, 2013 was $US9.3 billion ($A10.3 billion) after taking into account cash on hand of $2.8 billion and excluding finance leases of $600 million.
Earlier this month, the company said it was investigating the death of Zuvela to make sure similar incidents never happened again.
Power responded to a Department of Mines statement identifying "cultural issues" in the company, clarifying that the government's comments were related specifically to smaller contractors and how they worked on FMG sites.
FMG said safety isolation and lock out/tag out procedures would be a focus for its own review while it also assisted the government investigation.
Shares in FMG and MinRes last closed at $A5.14 and $11.37, respectively.