Sir Ian replaces Sir Victor Blank, who left in January after eight years to become chairman of Lloyds TSB.
As well as working for Ford and Nissan, where he brought the production of Japanese cars to the UK, Sir Ian has also been deputy chairman of supermarket chain Asda and a director of the Bank of England.
Most recently, he was chairman of plasterboard maker BPB until its takeover by Saint-Gobain at the end of 2005.
He currently holds non-executive directorships at engineering firm GKN and baking business Greggs and is also the senior non-executive director at financial group Northern Rock.
Sir Ian formally takes up his post after Trinity Mirror's annual general meeting on 4 May.