The Jane Eyre actress will star in the comedy project alongside Social Network actor Jesse Eisenberg.
The Double, co-financed by Film4, is the story of a man driven to near breakdown by the appearance of his doppelganger. The project was inspired by the Fyodor Dostoyevsky novella of the same name.
Ayoade - who made a name for himself with The Mighty Boosh and The IT Crowd - made his directorial debut in 2010 with Submarine, an adaptation of Joe Dunthorne's Welsh coming-of-age novel.
"Richard's joyous debut film, Submarine, established him as a unique voice and so we are really delighted to be supporting his next project, The Double. With Jesse and Mia now on board, it promises to be a wonderful journey," said Channel 4's head of film and drama Tessa Ross.
The Double will shoot in the UK in spring/summer this year.
Watch the Submarine trailer below: