McKay has signed on to direct the untitled project from his own script, and he plans to begin shooting in the spring, reported Deadline.
Pitt will co-produce the project alongside McKay, Dede Gardner, Will Ferrell, and Jeremy Kleiner under his Plan B company.
McKay, who teamed up with Pitt for last year's "The Big Short", is planning to release the movie next year.
"I've always found Cheney fascinating. Questions of what drove him, what his beliefs were; but once we started digging I was astounded at how much he had shaped modern America's place in the world and how shocking the methods were by which he gained his power," the filmmaker said.
He served as Vice-President under Bush from 2001 to 2009.
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