The Oscar-nominated An Education actress will play a woman who ends up on the run with a Hollywood stuntman-turned-getaway driver after a bank heist goes wrong.
Breaking Bad's Bryan Cranston is also closing in on a role in the Universal project.
Nicolas Winding Refn (Bronson) will direct Drive based on James Sallis's novel.
Mulligan can next be seen playing Gordon Gekko's daughter in Wall Street: Money Never Sleeps. Her drama Never Let Me Go will open the BFI London Film Festival on October 13.