When he launched the government's higher education framework last week, Lord Mandelson set out a vision of universities with a clear focus on science and engineering skills and stronger links with business.
So Lord Browne, who became a BP apprentice after a physics degree at Cambridge University and went on to become chief executive of the oil giant, and President of the Royal Academy of Engineering, could be seen as a natural choice to head the review of tuition fees.
Lord Broers, past president of the academy (and former Cambridge Vice Chancellor) said John Browne would bring what he called "his formidable intellectual rigour" to the review as well as his experience of international engineering and business at the highest level.
Lord Browne, who has a string of honorary degrees, had a deep and wide understanding of higher education in the UK and globally, he said.
But Lord Mandelson was equally at pains to deny a "utilitarian" agenda in which universities were economic engines producing graduates to meet industry's skills needs.
Universities were there "to provide us with both civilisation and competitiveness", he said.
And Lord Browne, aged 61, lists among his interests opera and the arts. He is a trustee of the British Museum and of the Tate Gallery in London, among others.
Lord Broers said of him: "His involvement with our national art and museum collections means that he knows the importance of culture and the arts."
He had a 40-year career with BP, rising to be chief executive, from 1995 - and, people say, Britain's most outstanding businessman.
BP's name was tarnished by an explosion at a Texas refinery in which 15 died and some 170 were injured, environmentally damaging oil pipeline leaks in Alaska and a propane price manipulation scam which led to a $303m fine by the US Commodity Futures Trading Commission.
But mention Lord Browne in business circles and what people recall is his sudden unseemly departure from BP in 2007 after it emerged he had lied to the High Court about how he had met his young former lover, Jeff Chevalier - who was telling his story of their lavish lifestyle to a newspaper.
As chair of the tuition fees review he will have to contend with suspicions of the student community towards what National Union of Students president Wes Streeting called a "stitch up".
But he might be the right man for such a challenge, as his negotiating skills contributed to what commentators describe as the "stellar" expansion of BP via a series of acquisitions.
BP's share price more than quadrupled during the 1990s. But he did also oversee severe cost-cutting at the company.
Can someone with a penchant for fine wine, whose Desert Island Discs luxury was a lifetime's supply of "great cigars", have a natural empathy with the average student?