The company paid US$1.4 billion up-front, funded from cash on hand and an $800 million acquisition debt facility.
A further $500 million is payable at threshold copper production rates and prices in 2022-25.
South32 CEO Graham Kerr described the acquisition as a major milestone for the company.
"By adding copper to our portfolio, along with our recent commitments to substantially increase our green aluminium production, we are making significant progress reshaping our portfolio for a low carbon future," he said.
"Sierra Gorda will immediately contribute to earnings, improve group operating margins and give South32 long term exposure to a metal that is increasingly hard to discover, develop and produce.
We believe copper will play a key role in the world's decarbonisation and energy transition."
South32 expects the mine to contribute 27,000 tonnes of copper, 400t of molybdenum, 10,000 ounces of gold and 225,000oz of silver this financial year at unit costs of $1.63 per pound of copper equivalent.
"Safe and reliable" capital expenditure for the remainder of the financial year is forecast at $50 million, while improvement and life extension capex is forecast at $15 million.
Polish miner KGHM Polska Miedz holds the other 55% of Sierra Gorda.
