Ukrainian state-owned energy firm Naftogaz said Wednesday Russia's Gazprom would have to pay it $2.56 billion after a Stockholm court found in Naftogaz's favor in the final stage of a long-running legal battle.

In June 2014, Gazprom and Naftogaz lodged multi-billion-dollar claims against each other with the Stockholm arbitration court, which resolves commercial disputes.

The disagreement was a by-product of the worsening relations between Kiev and Moscow since Russia's annexation of Crimea and the eruption of Russian-backed separatist violence in Ukraine's Donbass region, which has killed more than 10,000 people.

The latest ruling in Stockholm, which concludes the legal dispute, centered on Naftogaz's claims that it was owed compensation for Gazprom not pumping a certain volume of gas per year via Ukraine and paying too little for what it did send through Naftogaz pipelines.

"Naftogaz was awarded damages of $4.63 billion for Gazprom's failure to deliver the agreed transit gas volumes," Naftogaz spokeswoman Olena Osmolovska said. There was no immediate comment from Gazprom.

Since the court previously ordered Naftogaz to pay Gazprom for gas supply arrears, the net payment Gazprom will have to make to Ukraine is $2.56 billion, Osmolovska said.

The Arbitration Institute of the Stockholm Chamber of Commerce does not publish or comment on its rulings, leaving it up to parties involved to go public if they want to.

In previous rulings, the court denied Gazprom's claim linked to a 'take-or-pay' clause that required buyers to pay for gas whether they take physical delivery or not, and found in Naftogaz's favor in terms of pricing.

But it also ordered Naftogaz to pay $2 billion to Gazprom for the gas arrears and ruled that it should buy 5 bcm of gas from Gazprom annually from 2018.