The company was previously owned by the Ebrahimi family, which bought the software developer from founder Tim Gill in 2000. The sale to Platinum was an all cash deal.
Platinum, which was founded in 1995 by US billionaire Tom Gores, is a global firm specialising in the merger, acquisition and operation of companies across a broad range of sectors, including IT, telecomms, publishing, logistics, manufacturing and distribution.
According to Platinum partner Brian Wall, who led the Quark acquisition team, the firm is already working with Quark's management to create an acquisition strategy focused on expanding the breadth and depth of Quark's product capabilities and geographical coverage.
Raymond Schiavone, president and chief executive at Quark, said: "This transition comes at an exciting time for our company and our customers. In the past few years we have made great strides in helping our customers realise dynamic publishing, have re-invigorated QuarkXPress, and are ready to take an early leadership position in digital publishing.
"Platinum Equity is well-positioned to help us continue to execute our dynamic publishing vision through their market reach, merger and acquisition experience, and operational support. This is the natural next step for Quark’s evolution."
Quark, which launched the first version of QuarkXPress in 1987, was once the dominant force in the desktop publishing market, before losing ground to rival Adobe Systems' InDesign and associated Creative Suite applications.
Wall said: "Quark is a legendary brand that helped create the desktop publishing market and is now helping organisations transform how they publish content both to print and digital media.
"Quark is committed to its loyal and dedicated user base and we are enthusiastic about the company’s new products which are gaining traction and generating positive reviews. We believe that with their expertise and innovative software, Quark has the potential to revolutionise publishing again."