Canada pledges $31bn in compensation for indigenous Canadians
In September, a top court upheld a 2016 ruling that the government underfunded First Nations services compared with those for non-indigenous children.
It ordered C$40,000 ($31,350; £23,340) payouts to each child who was in the on-reserve welfare system after 2006.
The government initially said it would appeal the verdict.
But it has come under intense public scrutiny after the discovery of over 1,100 unmarked graves at the sites of former residential schools.
Until as recently as 1996, Canada's residential school system separated indigenous children from their families and sent them to boarding schools where many were malnourished, beaten and sexually abused.
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The school system was part of attempts to assimilate indigenous children - forcing them to abandon their native languages and convert to Christianity.
The government's compensation amount, expected to be formally announced on Tuesday, will be used to settle the 2016 tribunal, two other lawsuits, and fund long-term reforms in the indigenous child welfare system, a source told public broadcaster CBC.
RoseAnne Archibald, National Chief of the Assembly of First Nations, said: "Money does not mean justice, however, it signals that we are on the healing path forward."
She added: "The magnitude of the proposed compensation package is a testament to how many of our children were ripped from their families and communities."
Some 150,000 First Nations, Métis and Inuit children were housed in the schools, which operated between 1874 and 1996.
The policy traumatised generations of indigenous children, who were forced to abandon their native languages, speak English or French and convert to Christianity.
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Christian churches were essential in the founding and operation of the schools. The Roman Catholic Church in particular was responsible for operating up to 70% of residential schools, according to the Indian Residential School Survivors Society.
Earlier this year, the Vatican said Pope Francis had agreed to visit Canada to assist with reconciliation efforts.
But a formal date has not been announced, and the Pope has not issued an official apology for the Church's role, despite repeated called by Canadians.