International production director Sharon Simpson described him as a "hard act to follow and a huge loss for me and the team".
Economist editor John Micklethwait said: "He has saved us repeatedly and seems somehow to understand us and our idiosyncrasies."
Mann's final official task was overseeing last week's issue, which had five possible cover variations and was printed at St Ives Peterborough on Friday morning (7 May) instead of its usual Thursday slot because of the General Election.
He is now planning to take a sabbatical and is looking into various publishing and production projects. Assistant production manager Amy Brown will step up into Mann's role.