Channing Tatum, star of the film, confirmed the news on Twitter. Released in 2012, the film was based on the actor's early days as a male stripper.
Tatum, 33, will produce the musical alongside Soderbergh, Magic Mike writer Reid Carolin, Gregory Jacobs and Nick Wechsler.
The production team are also working on a sequel to the film.
Tom Kitt and Brian Yorkey, creators of award-winning show Next to Normal, have been signed up to write the songs, while Roberto Aguirre-Sacasa will pen the book.
The Glee writer co-wrote Spider-Man: Turn Off the Dark and the upcoming musical version of American Psycho.
Magic Mike was self-financed by Tatum and Soderbergh and was made for $7 million (Â£4.5m).
It went on to become a surprise hit, making $167m (Â£109m) from global ticket sales.
This month Tatum was named the second highest-paid actor in the world by Forbes magazine.
It estimates he earned $60m (Â£39m) last year, mainly from Magic Mike. It also reports that a chain of Magic Mike bars are in the pipeline.
A stage musical based on the Steven Soderbergh film Magic Mike is to open on Broadway.