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Downie, 53, who was diagnosed with terminal brain cancer in 2015, died on Tuesday night (local time) surrounded by his family, according to a family statement.
"We are less of a country without Gord Downie in it," Trudeau said in Parliament.
Downie was known for his frenetic stage presence and telling long stories in the middle of songs. Formed in the 1980s with roots in blues and rock, the Tragically Hip found radio popularity on both classic and alternative rock stations.
The Hip, as it was widely known, held an emotional farewell tour last year after Downie's cancer was revealed, with the band's last hometown show in Kingston, Ontario, billed as a national celebration.
On Wednesday, radio stations played Tragically Hip songs as news of his death spread across the country, and tributes poured in on social media as Canadians remembered their encounters with Downie.
The National Hockey League Players' Association tweeted thanks to Downie, saying his music was "the soundtrack of car rides to practices, bus trips to tournaments, and dressing rooms across Canada. Hockey was part of you and you will always be part of hockey."
Perry Bellegarde, national chief of the Assembly of First Nations, tweeted prayers for Downie's family, adding that "our hearts break on news of the passing of ... an ally and friend."
Downie had become an outspoken supporter of Canada's indigenous people, penning songs about the painful legacy of colonialism and urging Canadians towards reconciliation.
In their statement, Downie's family said the singer had spent his last days making music and memories with family and friends.
"Thank you everyone for all the respect, admiration and love you have given Gord throughout the years - those tender offerings touched his heart and he takes them with him now as he walks among the stars," the statement said.