The Staffordshire-based business employs 600 people across five manufacturing sites and two distribution centres.
Inflexion managing partner Simon Turner said: "The team at Marley have done a phenomenal job in creating not only a truly market-leading product, but also a resilient and differentiated business model in an industry with very attractive dynamics. The brand is exceptionally well regarded, and we look forward to drawing upon our industry experience as we partner with management to build on Marley's strong market position and product range."
Marley general manager David Speakman added: "We are extremely proud of our long heritage and are very excited by the opportunities to grow the company further. Inflexion's industry knowledge gleaned through its investment in builders merchants Huws Gray means they truly understand our sector, while their experience in helping expand businesses organically and acquisitively make them an excellent fit for our next stage of growth."
The acquisition is expected to complete next week.