The 82-year-old singer's death was "sudden, unexpected and peaceful", Robert B Kory said in a statement.
No cause was given by the family when Cohen's death was announced last week.
The statement said that Cohen died on 7 November - three days before an announcement was made to the public. He was buried in Montreal on 10 November.
"With only immediate family and a few lifelong friends present, he was lowered into the ground in an unadorned pine box, next to his mother and father,'' the singer's son Adam Cohen wrote last week.
Leonard Cohen's representatives say a memorial in Los Angeles is being planned.
Canadian Prime Minister Justin Trudeau led worldwide tributes to the singer, who was known for songs including Hallelujah, Suzanne, Bird on the Wire and I'm Your Man.
He released his 14th album, You Want It Darker, just last month.
Canadian singer, songwriter and poet Leonard Cohen died in his sleep after falling during the night at his Los Angeles home, his manager has said.