The deal was approved by Turquoise Hill shareholders earlier this month.
The deal leaves Rio Tinto holding 66% of Oyu Tolgoi outright. The remaining 34% is held by the Mongolian government.
"This acquisition further strengthens our copper portfolio, as part of our strategy to grow in materials the world needs for achieving net zero and delivering long-term value for our shareholders," Rio Tinto Copper chief executive Bold Baatar said.
"We now have a simpler and more efficient ownership and governance structure, with our partner the government of Mongolia, as we proceed together towards sustainable production from the underground mine."