He joined the Sunday paper a year ago, following a stint as executive editor of The Independent.
Prior to the Independent, Mullin was deputy editor of The Scotsman, and Ireland correspondent for The Guardian.
Ivan Fallon, chief executive of Independent News & Media UK, said: "John has already stamped his own brand of journalism on our Sunday paper, with a focus on news and news analysis.
"He is a true professional, with a deep knowledge of how newspapers should be put together. The Independent on Sunday has always punched above its weight in a very competitive Sunday market, and will do so even more effectively under John's leadership."
Mullin said: "These are challenging times, but I take over a paper in robust health and with a hugely committed and energetic staff, and I relish the task ahead."
His appointment follows a further slide in the IoS's circulation. In the December newspaper ABCs, the paper's circulation was down by 2.53%, meaning it dipped below the 200,000-copy mark for the first time in the second quarter of 2007.