She will report into editor-in-chief Lucie Cave, and replaces Jeremy Mark, who left in March after two and a half years in the editor’s chair.
Cox said: "Heat is an icon of a brand and I'm honoured to be working with Lucie and the amazing team on such a well-loved, generation-defining title. I have lots of ideas for the development of the magazine and can't wait to get started."
Cox began her career in young women’s magazines, working at Smash Hits, 19 and Mizz. She has also been features director at Grazia and acting deputy editor of News UK's Fabulous magazine. She has spent the past four years at Cosmopolitan.
She is also a young adult fiction writer, creating The Dead Girls Detective Agency series for HarperTeen.
Cave said: "Suzy is a very talented editor, full of brilliant plans for Heat, and I am very much looking forward to working with her. She is joining Heat at a very exciting period in its history as we continue to evolve."
Cox's start date will be confirmed shortly.
Earlier this month, Heat won a PPA Award for Best Use of Social Media.
In the last six months of 2014, Heat saw a 6.9 per cent drop in its circulation to 203,728. This was a 15.6 per cent drop year on year.