Wallace, who was previously the deputy editor of the Sunday Mirror, replaces Piers Morgan, who was sacked last month. Morgan was fired after pictures published in the Daily Mirror showing the torture of Iraqi prisoners turned out to be fakes.
Reports suggested Mirror Group approached the News of the World's editor, Andy Coulson, and Simon Kelner, The Independent's editor-in-chief, before hiring Wallace.
Wallace, 43, worked for more than a decade at the Mirror as its show-business editor and then its US editor before joining the Sunday Mirror, where he has been the acting editor throughout Tina Weaver's maternity leave.
The Mirror's deputy editor, Des Kelly, who replaced Morgan on a temporary basis, has left, leaving Wallace free to appoint his own deputy.
Trinity Mirror also announced it was promoting Ellis Watson, the general manager of national newspapers, to managing director of national newspapers.
The move sees the Trinity Mirror chief executive, Sly Bailey, take a back seat in the running of the national newspapers - editors of the UK national titles will now report directly to Watson.
A key task for Wallace and Watson will be to address the long-term circulation decline of the Mirror. Its May circulation was down 6 per cent to 1,846,734.
Wallace said: "The greatest challenge for national newspapers is circulation. I'm confident that we have the team, the talent and the will to tackle this challenge."