The company achieved its share purchase target of 41.2 million shares for A$2.87 billion.
The buy-back price was $69.69, a 14% discount to the market price.
Rio CEO J-S Jacques said the company was delighted to return cash to shareholders.
"Strong demand has enabled us to return the maximum amount, and at a discount of 14%," he said.
"The remaining US$1.1 billion of funds will be returned through our ongoing buy-back of Rio Tinto plc shares.
"In 2018 we have announced cash returns to shareholders of US$6.4 billion. Our strategic focus, with disciplined allocation of capital, is ensuring that we continue to deliver superior returns to our shareholders in the short, medium and long term."
Rio also announced today the completion of the the lease and sale of a wharf and land in Kitimat, British Columbia, to LNG Canada for $576 million.
LNG Canada, a joint venture comprising Shell, PETRONAS, PetroChina, Mitsubishi Corporation and KOGAS entered into an option agreement with Rio in 2014 for various options to lease or purchase the wharf and areas of land.
"This sale demonstrates our ability to generate cash from an existing asset, without losing future cash flow, as we continue to drive value across our entire portfolio," Rio chief financial officer Jakob Stausholm said.
LNG Canada will construct a replacement wharf for Rio to export shipments of aluminium from the BC Works smelter.
Rio shares opened at A$81.23.