The province was the first in Canada to adopt right-to-die legislation last summer, making doctor-assisted death legal as part of a comprehensive end-of-life bill expected to go into effect by December at the latest.
Gaetan Barrette said Friday the ruling from the high court is clear.
"This situation is clearly resolved across the country and we're quite happy the conclusion is such and we expect all provinces to go forward in our direction," Barrette told a news conference in Quebec City.
Barrette said the ruling serves as vindication for Quebec politicians, who were routinely criticized in the rest of Canada when they began debating the issue of doctor-assisted death in 2009.
Quebec held highly divisive public hearings in 2010 and 2011 on the matter and concluded terminally ill patients be allowed to die in exceptional circumstances.
The bill was passed last June with all-party support and sets out the strict conditions under which a doctor would administer "continuous palliative sedation" until death.
The province has said it is on sound legal footing as the bill is an extension of end-of-life care, making it a health-care issue which falls under the province's jurisdiction.
Patients would have to have an incurable illness and be in an "advanced state of irreversible decline in capacities."
They would also have to demonstrate they are in constant physical and psychological pain which doctors could not treat with medications.
The attending physician would have to supervise the request, in conjunction with a hospital medical team.
A patient could change their mind and withdraw or postpone the request at any time.
Veronique Hivon, the Parti Quebecois member who spearheaded the bill, says Quebec's work might serve as a "recipe to follow" for other provinces.
"I think it confirms that Quebec was right in the first place to have the debate, Quebec was right to do it the way it did it," Hivon said.
Hivon told reporters there is no longer a sword of Damocles hanging over Quebec's law and that the Supreme Court ruling actually goes further than what Quebec has proposed.
The high court ruling does not limit physician-assisted death to those suffering a terminal illness.
"In Quebec, we will be able enlarge the scope and it's something we'll have to look at," Hivon said, adding the issue wasn't constitutionally clear when the province drafted their own bill.
Jean-Pierre Menard, a lawyer who specializes in health-care, said Friday's court decision should reassure doctors who were worried about the legality of Quebec's end-of-life legislation.
Menard was among a panel of experts who determined the province had the legal jurisdiction to legislate in matters of health.
He said lawyers need to keep a watchful eye over the Harper government in order be assured federal politicians don't try any "tricks" to circumvent the Supreme Court decision and Quebec's new law.
"There are no more obstacles keeping Quebec's law from coming into effect," he said.
Barrette said there is still a legal challenge pending against the Quebec government and could be impacted by Friday's ruling.
Two Quebec-based organizations are challenging on the grounds that the law undercuts sections of the Criminal Code that outlaw assisted suicide and euthanasia.
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