Record label Sony Music said it was proud to have "celebrated Cohen's artistry" over his six-decade career.
"Leonard Cohen was an unparalleled artist whose stunning body of original work has been embraced by generations of fans and artists alike," it said in a statement.
"The Sony Music Canada family joins the world in mourning Leonard Cohen's passing."
Cohen's songs included Bird On The Wire, Hallelujah and So Long Marianne, written about his lover and muse Marianne Ihlen, whom he met in Greece in the 1960s.
She also inspired the song Hey, That's No Way To Say Goodbye.
In July this year, when he heard that Ihlen was near to death, he wrote to her: "Well Marianne, it's come to this time when we are really so old and our bodies are falling apart and I think I will follow you very soon."
Singers, writers and politicians paid tribute to Cohen on social media.