The American actress and singer, best known for her roles in Ugly Betty and Desperate Housewives, said bringing "fashion's most terrifying editor-in-chief" to life is "an absolute dream".
The musical, based on the Oscar-nominated film and novel by Lauren Weisberger, will showcase an original score by Sir Elton John with lyrics by singer-songwriter Shaina Taub.
The 2006 film grossed nearly $A500 million worldwide and earned two Academy Award nominations.
The multiple Grammy-nominated 60-year-old said: "Bringing Miranda Priestly to life in the West End is an absolute dream come true. Gird your loins, folks."
The musical also boasts direction and choreography by Tony award winner Jerry Mitchell, a book by Kate Wetherhead and costume design by Gregg Barnes.
It is produced by Kevin McCollum, Rocket Entertainment, David Furnish and Jamie Wilson, with a special arrangement by Buena Vista Theatrical.
The musical first premiered in the US in 2022, with Beth Leavel playing the role of Miranda Priestly.
Sir Elton John has previously composed music for Broadway musicals such as The Lion King, Aida and Billy Elliot.
The Devil Wears Prada will premiere at London's Dominion Theatre in October 2024, preceded by an exclusive preview at Theatre Royal Plymouth in the summer.
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