Mr Morneau said the deal with Kinder Morgan is likely to be closed by August 2018.
It plans to seek a buyer.
"At the appropriate time, Canada will work with investors to transfer the project and related assets to a new owner or owners", he said.
Kinder Morgan last month gave Ottawa an ultimatum: Chairman Steve Kean said the company would suspend all work on the expansion project entirely if the legal issues surrounding it can not be resolved by May 31, adding that it would not continue risking shareholder funds on the project unless the clouds over it clear.
The Liberal government says it doesn't intend to be a long-term owner of the Trans Mountain expansion project.
Kinder Morgan set the deadline in part due to frustrations with delays caused by the British Columbia government, which is concerned about possible oil spills.
Canada first offered earlier this month to indemnify the expansion project before making Tuesday's announcement.
"We have agreed to a fair price for our shareholders and have found a way forward for this national interest project", said Steve Kean, chief executive officer of Kinder Morgan Canada and its parent, Kinder Morgan Inc (KMI.N).
Alberta has also agreed to provide funding for any unexpected costs that arise during construction.
Ottawa has the constitutional authority to build interprovincial projects like pipelines, but B.C. Premier John Horgan has gone to court to get a judge to weigh in on whether B.C.'s jurisdiction for the environment would allow him to regulate what flows through the pipeline.
After her arrest, May said permits issued for the twinning of the existing Trans Mountain pipeline did not respect the rights of Indigenous people. Currently, he said yesterday, Canada is losing US$11.56 billion (C$15 billion) annually because of the pipeline constraint.
Morneau said more investment will be needed to complete the construction of the pipeline expansion, and that in the long term the project "has commercial value" and should be in the private sector.
Financing will come from Export Development Canada. A lack of capacity in pipelines or in rail cars to ship oil produced in Alberta is also hurting Canada's energy sector.
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