Last month, South32 agreed to pay Sumitomo $1.55 billion cash for a 45% stake in the mine, as well as price-linked payments of up to $500 million until 2025.
KGHM holds 55% of the mine and had a pre-emptive right over Sumitomo's stake, which it will not exercise.
South32 expects the deal to close in early 2022.
Sierra Gorda is expected to produce 180,000 tonnes of copper, 5000t of molybdenum, 54,000 ounces of gold and 1.6 million ounces of silver this year.
Shares in South32 were up 0.8% to A$3.59 this morning, valuing the diversified miner at $16.7 billion.