Mr. Turner is expected to assume the new post in October.
He and Ms. Bain will fill the seats left vacant following the recent resignation of Justice Jon Lyons and the departure of Justice Cheryl Albury, who is scheduled to leave at the end of the year.
Sir Burton Hall, who also serves as chairman of the Judicial and Legal Services Commission (JLSC), said he thinks both of the attorneys would add much experience to the bench.
"I can confirm that the governor-general has accepted the advice of the commission that Mr. Turner assume office as a justice as of October 1," he said.
"Indeed, the only reason why you may be hearing that for the first time now is that we are still in the process of drafting the press release."
The chief justice said Ms. Bain will assume office on August 14.
"The governor general acceded to my advice and I can say that definitively because as the chairman I signed the advice and confirmed their acceptance," he said.
As for Sir Burton, he was recently nominated to become a permanent judge of the International Criminal Tribunal for the former Yugoslavia (ICTY).
He is scheduled to take up his new post in August.
