Born in Montreal in 1934 into a prosperous Jewish family that founded synagogues in Canada, Cohen maintained a strong connection to the city despite having spent much of his young adulthood on the Greek island of Hydra before pursuing a enviable music career in Los Angeles, California.
Shortly after his death was announced, dozens of fans converged spontaneously around Cohen's home in Montreal, lighting candles and leaving flowers as well as one of the top-hats that were his signature look late in his career.
Young and old, Cohen's fans played some of his best-known songs on their smartphones. A wire hanging on the front door read out the letters "H-A-L-L-E-L-U-J-A-H."
Canadian Prime Minister Justin Trudeau mourned Cohen, long considered one of the country's foremost writers, as a "remarkable Montrealer."
"Leonard, no other artist's poetry and music felt or sounded quite like yours. We'll miss you," Trudeau said in a statement.
Trudeau said that Cohen would be "fondly remembered for his gruff vocals, his self-deprecating humor and the haunting lyrics that made his songs the perennial favorite of so many generations.
"Leonard Cohen is as relevant today as he was in the 1960s. His ability to conjure the vast array of human emotion made him one of the most influential and enduring musicians ever. His style transcended the vagaries of fashion," Trudeau said.
Montreal Mayor Denis Coderre ordered the city's flags to fly at half-mast.
A storied musician and poet
After studying literature, Cohen began as a poet before seeking a more stable career, comparatively speaking, as a musician. While at first receiving a lukewarm reception, Cohen went on to become a critical favorite with meditative songs such as "So Long, Marianne" and "Suzanne."
"Hallelujah," an anthem of uplift rich in biblical reference, has been covered by a vast array of artists including Jeff Buckley, John Cale, k.d. lang and Rufus Wainwright.
In an industry where many artists burst onto the scene with a supernova of activity in their 20s and then dine out on past glories for decades, Cohen released some of his most vital work after age 50.
Like David Bowie, Cohen signed out with a final album. He released his 14th studio album, You Want It Darker, in October 2016, which featured the singer reflecting at length on his own mortality and which his son helped to produce.
"My father passed away peacefully at his home in Los Angeles with the knowledge that he had completed what he felt was one of his greatest records. He was writing up until his last moments with his unique brand of humour," said his son, Adam, in a statement.
The Recording Academy, which in 2010 presented Cohen with a lifetime achievement Grammy, mourned him as "one of the most revered pop poets and a musical touchstone for many songwriters."
"His extraordinary talent had a profound impact on countless singers and songwriters, as well as the wider culture," Academy president Neil Portnow said in a statement, adding, "He will be missed terribly."
Outside of Canada, Cohen enjoyed an international fan base and toured globally over the years to great success. For example, he was much admired in 1960s France, when French President Georges Pompidou was reputed to take his LPs on holiday. And it was said that if a Frenchwoman owned one record, it was likely to be by Cohen.
His record label announced on Thursday that a private memorial service for the artist was planned in Los Angeles.