The motion came a week after a historian wrote that a Supreme Court chief justice in the early 1980s provided information to the Canadian and British governments on the discussions between magistrates about the legality of repatriation.
Frederic Bastien suggested in a new book that Bora Laskin and another Supreme Court justice violated the principle of separation of executive and judicial powers.
On Tuesday, all 108 members of Quebec's legislature voted in favour of the motion. They represented the Parti Quebecois, the Liberals, the Coalition for Quebec's Future, and Quebec solidaire.
All provinces except Quebec, which was then led by sovereigntist premier Rene Levesque, endorsed the 1982 Constitution.
Tuesday's motion called for more details on the events that led to the adoption of the constitutional law of 1982.
Ahead of the vote, Premier Pauline Marois said Bastien's book reveals "very serious irregularities."
"It appears, in effect, that the chief justice of the Supreme Court communicated details to members of executive powers on the state of ongoing deliberations during the referral of 1981," said Marois, whose PQ holds a minority government.
"These actions raise the delicate question of the independence of the highest court of Canada."
The Supreme Court of Canada announced last week it was looking into the allegations.
A spokesman for Prime Minister Stephen Harper has already dismissed a Quebec government request to have the documents in question made public.
The Conservative government also indicated last week Ottawa isn't going to revisit history and plans instead to concentrate on jobs and the economy.
On Tuesday, NDP Leader Tom Mulcair told reporters in Ottawa that it's understandable Quebec's national assembly voted unanimously in favour of having more light shed on the subject.
"It's what everyone wants," said Mulcair, whose New Democrats hold 57 seats in Quebec, by far the most seats of any federal party in the province.
"But the Supreme Court says it will take a first look at it. We'll see what they tell us. But for my part, I remain, like I said on the weekend, roundly preoccupied as a lawyer, as a Canadian, as a Quebecer."
Liberal Leader Justin Trudeau, whose father Pierre Elliott Trudeau was prime minister when the Constitution was repatriated, was also asked Tuesday about the Quebec vote.
"We have a government in Quebec that does whatever it can to develop a new myth, to open old battles," Trudeau told reporters in Ottawa.
"The Supreme Court has taken on this question and I look forward to what they will say after they examine what happened at the start of the 80s."
In his book, Bastien also wrote that Supreme Court justice Willard Estey secretly advised the British government in 1980 that the high court would address the issue.
Bastien gathered information during eight years of digging through documents, including British Foreign Office archives.
- with files from Alexandre Robillard in Quebec City and Joan Bryden in Ottawa