McKay is best known for directing the 'Anchorman' films, where he worked with 'Ant-Man' star Paul Rudd.
The film is slated for July 17, 2015, a date Marvel said last week would not be affected by Wright's surprise departure, said the Hollywood Reporter.
Wright left the project amid reports that Marvel Studios head Kevin Feige was unhappy with Wright's take on the project for weeks.
The film was originally set to begin shooting June 2, but the production was put on hiatus when Feige ordered revisions on the script, which Wright co-wrote with Joe Cornish.
In addition to Rudd, Ant-Man's cast also includes Michael Douglas, Evangeline Lilly, Michael Pena, Corey Stoll and Patrick Wilson.
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