Justice Paul Belanger will look into and report on events surrounding the collapse of the Algo Centre Mall and review the emergency management and response to the disaster, Gerretsen said in a statement Monday.
Once the inquiry has begun, Belanger will report back publicly within a year, he said.
Cabinet still has to establish the public inquiry, which will set out its scope, Gerretsen said.
"The government is actively engaged in finalizing the terms of reference and, once approved, will make them available to the public," he said in the statement.
Two women were killed when a section of the roof came crashing through the Algo Centre Mall on June 23.
Residents have complained that the mall was in shabby condition before the cave-in and have questioned the speed at which rescuers tried to reach those trapped in the rubble.
Police have also launched their own criminal investigation into the accident. The Ontario Ministry of Labour, which visited the mall six times over the last three years, is also conducting its own probe.
"I join the residents of Elliot Lake in hope that the independent inquiry will ask the tough questions about the collapse so we can ensure that nobody has to go through what our community experienced," said Michael Mantha, MPP for Algoma-Manitoulin, in a statement.
Gerretsen said Belanger has a long and distinguished judicial career that began in 1978. He served as a senior judge for Eastern Ontario from 1984 until 1990 and as a regional senior judge for the Ontario Court of Justice from 1996 until 2002.
Belanger has presided over several high-profile cases. He's perhaps best known for acquitting former federal privacy commissioner George Radwanski of criminal fraud charges in 2009.
Radwanski resigned after it was revealed he'd racked up thousands of dollars in travel and hospitality expenses.
Belanger also presided over the trial of Andre Dallaire, who tried to assassinate former prime minister Jean Chretien in 1995 after breaking into 24 Sussex Drive. He was confronted by Chretien's wife Aline, who went into the bedroom, locked the door and called the RCMP.
Belanger found Dallaire guilty of attempted murder, but not criminally responsible.
The Progressive Conservatives said Belanger needs to begin his work as soon as possible to restore the public's confidence in the province's emergency measures system.
"I think one of the surprises that I had and I know a number of other Ontarians had was when our public safety minister came out and said there was nothing wrong days before the inquiry was called," said Tory Steve Clark.
"I think all Ontarians and especially the people of Elliot Lake want those answers ... We want Justice Belanger to work quickly and I think we all want to find closure on just why that happened."