The arrangement was approved by approximately 86.6% of all votes cast as well as by approximately 60.5% of the shares voted by minority shareholders.
Turquoise Hill also reported that valid dissent notices were filed representing less than 17.5% of all outstanding shares.
"As such, the company currently expects that, subject to obtaining final approval of the Court...and assuming satisfaction or waiver of all other closing conditions, the Arrangement will be completed on or shortly following December 16," Turquoise Hill said.
"We welcome the support from minority shareholders, which is a key milestone in our acquisition of TRQ," Rio Tinto Copper chief executive Bold Baatar said.
"This transaction will deliver significant benefits for all shareholders, and allow us to progress the Oyu Tolgoi project in partnership with the government of Mongolia with a simpler and more efficient governance and ownership structure."
Rio already owns 51% of Turquoise Hill and in March, bid $34 per share for the remaining shares it didn't hold.
Turquoise Hill rejected that offer and Rio returned in August with a $40 per share bid.
In early September, the pair announced they had reached an in-principle agreement for a $43 per share buy-out, valuing the minority stake at US$3.3 billion.
On closing, Rio will hold 66% of the Oyu Tolgoi copper-gold operation in Mongolia, with the remainder held by the government.