Mr Gill has been with the magazine for five years, having joined as a reporter in 2007 and subsequently holding roles as deputy news editor and news editor.
Ms Mroz has been appointed digital publishing director within TSL Education, which also publishes the Times Educational Supplement.
"It's a huge honour to be taking over from Ann as editor," said Mr Gill. "She has been an inspiration to the whole team and has led the magazine's award-winning coverage of an incredibly tumultuous period in higher education.
"I will aim to continue where she has left off, producing a magazine that not only reports on the sector but is a vital part of it.
"As well as doing everything that good journalism should do - holding authority to account, scrutinising government policy and keeping readers abreast of news across the sector - it's also our aim to produce a magazine that surprises, entertains and celebrates its wonderful readership.
"That includes tapping into the intellectual debates and providing a forum for essays on as diverse a range of topics as possible."
He added: "We rely on readers talking to us and telling us of issues that we should be aware of, pitching ideas and writing for us in our features, opinions and books sections. We are always pleased to hear from them about what we are getting right and when we get things wrong."