Sophocles' classic play narrates the story of a man who unwittingly kills his father and marries his mother, and the two stars will lead Robert Icke's new version into London's West End next year, followed by a run on Broadway in New York.
Icke and Strong previously worked together in David Hare's play, "The Red Barn", at the National Theatre four years ago, and joined forces with producer Sonia Friedman to persuade Mirren to join the ensemble.
The director gushed to Britain's Daily Mail newspaper about the "great" chemistry between his two leads, confessing, "She's a really attractive, very lively, vivacious older lady."
It's not Icke's first venture with the play - he directed a Dutch version at the Internationaal Theater Amsterdam earlier this year, which then went to the Edinburgh Festival in Scotland, where it was performed with English subtitles.
The play, which features Oedipus as a modern-day politician, will open in the latter part of next year, with a theatre and dates yet to be announced.