Gilles Courteau, commissioner of the Quebec Major Junior Hockey League, announced the deal at a news conference on Thursday acompanied by Quebecor CEO Pierre Dion.
The value of the transaction was not disclosed but The Hockey News pegged it at between $20 million and $25 million.
The media conglomerate has bought the franchise from various businessmen as well as from Colorado Avalanche coach Patrick Roy.
Courteau also announced that, as of next September, the Remparts will play in a new Quebec City to be named after Quebecor (TSX:QBR.B).
"We're trying really hard to land an NHL team," Dion said. "If one day we get one, the operations of both teams would be integrated into the same organization.
"They would share the new arena, as is the case in other North American cities."
Quebecor currently owns 70 per cent of the QMJHL's Blainville-Boisbriand Armada and might to have to sell off the stake in the Montreal-area team.
The timeline for the sale would be made public at a later date.