The singer - who won the seventh series of the ITV talent show - will star alongside Beverley Knight in Memphis The Musical, currently playing at the Shaftsbury Theatre in London.
Matt will play DJ Huey Calhoun from 6 July.
The delighted star said: "I'm thrilled to be making my acting and West End debut in Memphis. From the first time I saw the show I felt I had a real connection with the character of Huey.
"It's no secret that I worked for many years before my breakthrough as a musician. I started my first band when I was 12 years old and spent at least 15 years recording albums and sending demos to record companies before finally having my voice heard. It was the united love from family and friends, similar to that at the heart of the Memphis story, that saw me through.
"I am truly honoured to be sharing the stage with the incredible Beverley Knight, I've admired her work for such a long time and can't wait to get started in the show".
Beverley added: "I can't wait to continue my Memphis journey into the autumn with Matt - who will be a fantastic addition to our Memphis family. We all know he has a "fantastical" voice; I think many will be wonderfully surprised by his ability on stage."
Memphis The Musical is scheduled run until 31 October 2015 with early plans in progress for a major tour of the UK and Ireland from Autumn 2016.
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