The singer has already started work on his debut album and will release it through both companies in what is being billed as an industry first.
Murs was mentored by Cowell in last year's X Factor series, which saw him reach the final but ultimately lose out to 18-year-old Joe McElderry.
In a statement, Syco's managing director Sonny Takhar commented: "We are thrilled to be involved with Olly. As an artist he ticks every box."
Epic's managing director Nick Raphael added: "[Olly] is a big personality and we hope to make a big record on which we can showcase his obvious talents."
Murs was first linked to Epic earlier this month. More recently, it emerged that Cowell was also keen to work with him.
The Epic label has signed X Factor artists in the past and currently has 2008 finalists JLS on its books.