The decision by the country's top court will end three decades of legal challenges by the Manitoba Métis Federation (MMF) against the federal government.
The court's ruling will be handed down Friday in Ottawa.
Aboriginal-rights lawyer Tom Berger, who represented the MMF in the case, has argued that Ottawa reneged on the promises it made to the Métis under the Manitoba Act, which created the province and brought it into Confederation.
Federal lawyers argued that the case should be thrown out because it is more than a century old.
MMF president David Chartrand says a court ruling in the federation's favour would heal a lot of old wounds.
"It will be a vindication for our people," he told CBC News on Thursday.
"It will be very clear our nation as a whole, you know, waited 143 years to find vindication and to find that Canada is now in a position where it realizes it did not fulfil its constitutional obligations."
The Manitoba Act, made in 1870, promised to set aside 5,565 square kilometres of land for 7,000 children of the Red River Métis.
The land deal was made in order to settle the Red River Rebellion, which was fought by Métis rebels struggling to hold onto their land amid growing white settlements.
Dream of Métis homeland destroyed
However, it took 15 years for the lands to be completely distributed, while the Métis rebels faced hostility from large numbers of incoming settlers.
The federal government ultimately distributed the land through a random lottery, destroying the dream of a Métis homeland.
In 2010, the Manitoba Court of Appeal upheld a lower court ruling that found the federal government did not violate its duty to the Métis.
The case then went to the Supreme Court of Canada, where lawyers for both sides presented their arguments in December 2011.
The Métis federation is requesting a declaration that the constitutional agreement was not upheld.
Chartrand said even if the court rules against the federation, the Métis will still claim a victory.
"It's a win for us no matter what. If we lose, it's not going to be because of history," he said.
"It's not because we were wrong. The land didn't come to our children. It's going to be on a technicality. It still will be, at the end of the day, an issue for Canada to resolve."