Fox, who takes on the position from 10 September, replaces former chief executive Sly Bailey who announced in April that she would be quitting her role at the group.
Having founded Office World, Fox had held the position of chief executive at HMV since 2006 and is currently a non-executive director of Guardian Media Group.
According to Trinity Mirror chairman David Grigson, Fox will provide "the strategic leadership the company needs".
He added: "His experience gives him a current and in-depth understanding of how consumers’ habits are changing and the technology that is driving these changes.
"He is a great team player and leader and his skills and experience perfectly complement those of the existing executive team."
Fox, who will be paid a base salary of £500,000 per annum with a maximum bonus of £375,000, replaces Bailey who took over the role in 2003 and is cited with leading the company through a number of cutbacks in its fight to survive the current economic crisis and changing world of publishing.
Commenting on his new role, Fox said he was "delighted" to be joining the group and had been impressed with the team at Trinity Mirror.
"Whilst the Group’s current financial performance is robust, we will need to continue to evolve the business to meet the changing needs of our customers," he added.
Earlier this month Trinity Mirror appointed Ian Dowds to the newly created role of managing director, media of its digital division.
Dowds, who also takes up his new role in September, will be responsible for the commercial and editorial development of Trinity Mirror Digital’s (TMD) publishing division.
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