The former actor, who started his directing career as Ken Loach's assistant, died on Wednesday in London.
Mackenzie was viewed by his peers as one of Scotland's most-talented film-makers. His early work included Just Another Saturday which documented conditions at Glasgow's shipyards and A Sense of Freedom, based on the autobiography of Glasgow gangster Jimmy Boyle.
The Long Good Friday, the story of a ferocious gangster who tries to organise a deal with the American Mafia to renovate London's docklands while his empire is destroyed from the inside, is widely acclaimed as the greatest gangster film in the history of British film.
Niall Fulton, senior programmer at the Edinburgh International Film Festival, said: "He was a formidable character, had a superb intellect and, without a doubt, one of the most important film-makers to come out of Scotland. John made a huge contribution to Scottish cinema and easily ranks alongside the finest in British cinema."
He was born in Edinburgh in 1932 and taught in the city before moving to London in 1960.