The government of Pakistan will have to pay the damages to Tethyan Copper, a 50:50 joint venture between Antofagasta and Barrick after the amount was decided by an international arbitration tribunal of the World Bank's International Centre for Settlement of Investment Disputes (ICSID).
"We remain willing to discuss the potential for a negotiated settlement with Pakistan and will continue to protect our commercial interests and legal rights until the conclusion of this dispute," said Tethyan Copper chairman William Hayes.
Tethyan Copper filed an arbitration claim over what it felt was an unlawful denial of a mining lease for Reko Diq in 2011 by the provincial government of Balochistan, which a feasibility study had indicated was one of the largest undeveloped copper and gold deposits in the world.
Compensation of US$4.1bn was decided with reference to the fair market value of Reko Diq at the time the mining lease was denied, plus interest of US$1.75bn and just under US$62mln of legal costs.
There are limited grounds for challenging the award under the ICSID convention.
Antofagasta said it did not expect to recognise the damages payment in its financial statements until the money had been received.
Shares in Antofagasta were up 4.5% to 901.73p in early trade on Monday.