Oliver has extensive experience in the financial industry, having served at the Ontario Securities Commission, Investment Dealers Association of Canada and Merrill Lynch.
At 73, he is one of the oldest cabinet ministers. Many had speculated that younger stars overseeing crucial files were among the strong candidates for the job.
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As the minister responsible for natural resources, Oliver has been Ottawa's biggest champion of the controversial Keystone XL pipeline to the United States, a project of TransCanada Corp. , and has clashed with environmentalists opposed to the project.
It was unclear who might replace Oliver and handle that file, which involves delicate diplomacy with the Obama administration.
Conservative Prime Minister Stephen Harper is expected to officially announce the appointment later on Wednesday.
Oliver inherits a federal budget that is on track to post a surplus in 2015, ahead of an election scheduled for October 2015. The Conservatives promised in 2011 to offer tax cuts for families with children once they had a budget surplus, although more recently there has been some debate over what form those tax breaks should take.
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Like Flaherty, Oliver represents an electoral district in the Toronto area, which will be critical in the 2015 election.
In addition to overseeing the country's finances, Flaherty was the minister responsible for the Greater Toronto Area, a role Oliver may be assigned as well.
Some government officials, speaking on condition of anonymity, speculated that Harper might want Oliver to be minister on an interim basis only, to carry the government through the election.