The 45-year-old filmmaker said "The Hitman's Bodyguard" actor was initially averse to playing the part but yielded to the makers' request after he learnt Wright was helming the movie, reported Vanity Fair magazine.
"I was scared. Gary was scared. He was on the vape. I was on the roll-ups. I didn't need to tell him what a great character it was or what a great script it was.
The film follows the initial days of Churchill's term as prime minister, as Hitler's grip on Europe is tightening and the British Parliament is weighing its failed policy of appeasement.
Also featuring Ben Mendelsohn, Kristin Scott Thomas and Lily James, "Darkest Hour" hits the screens on November 22.