The sale brings Freeport close to ending more than nine years of often fractious negotiations with Indonesia over ownership rights to Grasberg.
The agreement gives the parties six months to close the deal and process several permits including those related to antitrust laws in China.
Inalum Chief Executive Budi Gunadi Sadikin said at a press conference his company would be ready to complete the transaction in November.
Several matters must still be resolved before the share transfer, he said. "There are documents, administrative permits and there is the money," Sadikin added.
After the transfer Inalum will hold a 51.23 percent stake in PT Freeport Indonesia, which will then be issued with a special mining permit for Grasberg, ending its existing operating contract for the mine.
Inalum has the option of financing the transaction using a combination of bank loans, bonds and internal cash reserves, Sadikin said, noting that the composition would depend on interest rates at the time of the deal.
Freeport McMoRan Chief Executive Richard Adkerson told reporters the deal signed on Thursday is a "definitive sales and purchase agreement", which he hoped would end controversy surrounding Freeport's business in Indonesia.
"This completes the negotiations and fixes and binds issues that were not dealt with," he added. "Now the next step is to go to closing."
"We've responded to the government's ambitions, so our hope is that this allows us to stabilize our operations," Adkerson said.
Rio holds a 40 percent participating interest in the Grasberg mine, which will be converted to an equity stake that will be transferred to Inalum, as part of the transactions.
Freeport Indonesia Executive Vice President Tony Wenas earlier said he hoped the deal would be closed "this year."
(Reporting by Wilda Asmarini and Bernadette Christina Munthe; Writing by Fergus Jensen; Editing by Kenneth Maxwell, Joseph Radford and Alexandra Hudson)
By Wilda Asmarini and Bernadette Christina Munthe