The announcement comes more than 20 years after Irish writer Roddy Doyle was first approached about bringing his creation to the stage.
The 1991 film, which was directed by Alan Parker, tells the story of a group of misfits who start an unlikely soul band in Dublin
Speaking about the film's success, Doyle said: "The Commitments was something of a monster, particularly in Ireland... it was an immediate, huge success and at the time I think it was the most successful film ever released in Ireland.
"There was immediate interest then in doing a musical. But I don't think I had ever been to a musical and the ones I'd seen on television had never really grabbed my attention much."
He added: "In the house I live in at the moment if The Sound Of Music comes on all the males, including the dog, stand up and walk out while the females stay and cry. It's the same if any of those musicals come on."
The musical is due to open in October and will feature songs such as Mustang Sally.
Commenting on whether any of the original cast will appear in the stage version, Doyle said they were "too old."
"We're all mortal and I met a lot of them quite recently. Most of them accept that we're lacking in hair!"